{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 14 0 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "normal C" -1 262 "Times" 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 18 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 289 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 293 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 301 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 303 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 305 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 307 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 309 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 310 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 311 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 312 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 313 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 314 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 315 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Headi ng 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "List Item" 0 14 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 14 5 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }2 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 114 "\253 Do not worry about your difficulties in mathematics; I can assure you that mine are stil l greater \273 A. Einstein." }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 34 " Universit\351 Paris 7 - Denis Diderot" }}{PARA 0 "" 0 "" {TEXT -1 15 " Ann\351e 2000-2001" }}{PARA 256 "" 0 "" {TEXT 262 16 "MI 101 - Maple V " }}{PARA 257 "" 0 "" {TEXT 262 20 "Groupes A4 - A5 - D5" }}}{EXCHG {PARA 18 "" 0 "" {TEXT 263 60 "2. Nombres complexes, arthimetique, po lynomes et \351quations." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Sommai re:" }}{PARA 14 "" 0 "" {TEXT -1 21 "1. Nombres complexes." }}{PARA 14 "" 0 "" {TEXT -1 30 "2. Operations d'arithm\351tiques." }}{PARA 14 "" 0 "" {TEXT -1 28 "3. Caculs sur les polynomes." }}{PARA 14 "" 0 "" {TEXT -1 33 " 3.1 La commande factor(...)." }}{PARA 14 "" 0 "" {TEXT -1 34 " 3.2 La commande collect(...)." }}{PARA 14 "" 0 "" {TEXT -1 50 " 3.3 Autres commandes Maple sur les polynomes." }} {PARA 14 "" 0 "" {TEXT -1 13 "4. Equations." }}{PARA 14 "" 0 "" {TEXT -1 19 " 4.1 Equations." }}{PARA 14 "" 0 "" {TEXT -1 30 " 4.2 S yst\350mes d'\351quations." }}{PARA 14 "" 0 "" {TEXT -1 30 " 4.3 S olutions num\351riques." }}{PARA 14 "" 0 "" {TEXT -1 49 " 4.4 Les \+ commandes isolve(...) et msolve(...)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 293 5 "Note:" }}{PARA 0 "" 0 "" {TEXT -1 99 "On peut avec Maple assign er un nom \340 une expression plus compliqu\351e. Pour ce faire, on ut ilise le '" }{TEXT 291 2 ":=" }{TEXT -1 1 "'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(x);\nx := 5;\nevalf(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 128 "X aura la valeur 5 jusqu'\340 la fin des calcu ls. Si l'on veut rendre \340 un nom la valeur de variable, alors on ut ilise la commande " }{TEXT 292 14 "unassign(...) " }{TEXT -1 90 "Regar dez bien l'aide sur la commande unassign, ce n'est pas aussi \351viden t qu'il y parait. " }}{PARA 0 "" 0 "" {TEXT -1 58 "Notez que la comman de unassign ne renvoie pas de r\351sultat." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "unassign('x');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(x);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }} {PARA 4 "" 0 "" {TEXT -1 20 "1. Nombres complexes" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 "Maple sait faire des calculs sur les nombres complexes, I (\"i majuscule\") represente la racine de -1 en langage Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3+4*I;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a+I*b;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Voici quelques calculs qu e Maple sait r\351aliser :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "(2+5*I)+(1-I)+5*(3+6*I);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(4+6*I)*(7-9*I);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "(1+I)/(3-2*I);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "(2+8*I)^2;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 270 0 "" }}{PARA 0 "" 0 " " {TEXT -1 69 "Notez que Maple d\351compose toujorus le r\351sultat so us sa forum usuelle " }{XPPEDIT 18 0 "a+I*b;" "6#,&%\"aG\"\"\"*&%\"IGF %%\"bGF%F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "The comand " }{TEXT 256 5 "evalc" }{TEXT -1 124 " will evaluate and simplify complex numbers, again splitting a ny expression into its real and imaginary parts. The commands " } {TEXT 257 13 "evalc(Re(..))" }{TEXT -1 5 " and " }{TEXT 258 14 "evalc( Im(..)) " }{TEXT -1 143 "can be used to separately identify the real a nd imaginary parts of an complex expression. To find the complex conju gate of an expression, use " }{TEXT 259 15 "conjugate(expr)" }{TEXT -1 46 ". The modulus and argument may be found using " }{TEXT 260 6 "a bs() " }{TEXT -1 4 "and " }{TEXT 261 10 "argument()" }{TEXT -1 1 "." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 " La commande " }{TEXT 264 11 "evalc(...) " }{TEXT -1 100 "simplifiera u ne expression sous la forme d'une somme d'une partir r\351elle et d'un e partie imaginaire." }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande " } {TEXT 265 7 "Re(...)" }{TEXT -1 52 " donnera la partie r\351elle d'une expression complexe." }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande " } {TEXT 266 9 " Im(...) " }{TEXT -1 27 "donnera sa partie complexe." }} {PARA 0 "" 0 "" {TEXT -1 13 "La commande " }{TEXT 267 8 "abs(...)" } {TEXT -1 33 " donenra le module d'un complexe." }}{PARA 0 "" 0 "" {TEXT -1 13 "La commande " }{TEXT 268 14 "argument(...) " }{TEXT -1 21 "donnera son argument." }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande \+ " }{TEXT 269 15 "conjugate(...) " }{TEXT -1 41 "donnera le conjugu\351 d'un nombre complexe." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }{MPLTEXT 1 0 25 "evalc(2^(1+I));\nevalf(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalc(Im((3+5*I)*(7+4*I))); " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalc(co njugate(exp(I)));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "z := 2+3*I;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "abs(z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "argument(z) ;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Im(z); \nRe(z);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Un complexe peut etre \351galement represent\351 de fa\347on polaire, ie: sous la forme " } {XPPEDIT 18 0 "rho*exp(I*theta);" "6#*&%$rhoG\"\"\"-%$expG6#*&%\"IGF%% &thetaGF%F%" }{TEXT -1 5 ", o\371 " }{XPPEDIT 18 0 "rho;" "6#%$rhoG" } {TEXT -1 19 " est son module et " }{XPPEDIT 18 0 "theta;" "6#%&thetaG " }{TEXT -1 13 "son argument." }}{PARA 0 "" 0 "" {TEXT -1 60 "Pour avo ir une telle repr\351sentation, on utilise la commande " }{TEXT 271 6 "polar(" }{XPPEDIT 18 0 "rho;" "6#%$rhoG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT 272 1 ")" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "polar(2,Pi/4);\nevalc(%);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Pour convertir la forme \"usuelle \" en forme polaire, on utilise la commande " }{TEXT 273 19 "convert(. .., polar)" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "convert(2+3*I,polar);\nevalc(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 274 11 "Exercice 1." }}{PARA 14 "" 0 " " {TEXT -1 40 "a) Donnez une representation polaire de " }{XPPEDIT 18 0 "z[1] = 6+I*Pi;" "6#/&%\"zG6#\"\"\",&\"\"'\"\"\"*&%\"IGF*%#PiGF*F*" }{TEXT -1 1 "." }}{PARA 14 "" 0 "" {TEXT -1 48 "b) Donnez les parties \+ r\351elles et imaginaires de " }{XPPEDIT 18 0 "z[2] = (3-6*I)^(3*I);" "6#/&%\"zG6#\"\"#),&\"\"$\"\"\"*&\"\"'F+%\"IGF+!\"\"*&\"\"$F+F.F+" } {TEXT -1 22 ". Donnez son argument." }}{PARA 14 "" 0 "" {TEXT -1 102 " Donnez son module. Cela vous semble-t-il logique ? Trouvez un moy en de contourner le \"probl\350me\". " }}{PARA 14 "" 0 "" {TEXT -1 8 " c) Soit " }{XPPEDIT 18 0 "z[1] = -1+I;" "6#/&%\"zG6#\"\"\",&\"\"\"!\" \"%\"IG\"\"\"" }{TEXT -1 4 " et " }{XPPEDIT 18 0 "z[2] = 2*I;" "6#/&% \"zG6#\"\"#*&\"\"#\"\"\"%\"IGF*" }{TEXT -1 36 ", donnez le module et l 'argument de " }{XPPEDIT 18 0 "z[1];" "6#&%\"zG6#\"\"\"" }{TEXT -1 6 " et de " }{XPPEDIT 18 0 "z[2];" "6#&%\"zG6#\"\"#" }}{PARA 14 "" 0 "" {TEXT -1 12 " Mettre " }{XPPEDIT 18 0 "z[3] = z[1]/z[2];" "6#/&%\" zG6#\"\"$*&&F%6#\"\"\"\"\"\"&F%6#\"\"#!\"\"" }{TEXT -1 31 " sous forme alg\351brique. Mettez " }{XPPEDIT 18 0 "z[3];" "6#&%\"zG6#\"\"$" } {TEXT -1 18 " \340 la puissance n." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 29 "2. Operations d'arithm\351tique s" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 205 "Maple sait \351galement faire de nombreuses op\351rations d'arith m\351tique. Il peut faire des caculs modulaires ; calculer des pgcg et ppcm, donenr une factorisation d'un nombre en nombres premiers, deter miner le " }{TEXT 275 1 "n" }{TEXT -1 25 "i\350me nombre premier, etc. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 276 21 "2.1 Calcul modulaire." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "3+15 mod 4;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "1/3 mod 7;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Representation positive :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "modp(14,5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Represent ation symetrique :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "mods( 14,5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "le pgcd et le ppcm se claculent comment suit :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "igcd(6160,8372,56);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ilcm(38,341);" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Pour factoriser un nombre en nombres premiers :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ifactor(2850375285);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Po ur savoir si un nombre est premier :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "isprime(357649);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Pour connaitre le \+ " }{TEXT 277 1 "i" }{TEXT -1 19 "\350me nombre premier." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ithprime(5920);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 278 11 "E xercice 2." }}{PARA 14 "" 0 "" {TEXT -1 76 "a) Quel est le pgcd de 104 9427 et 17493 ? Ce pgcd est-il un nombre premier ?" }}{PARA 14 "" 0 " " {TEXT -1 131 "D\351composez 1049427 ;17493 et le pgcd en produit de \+ nombre premiers. Quelle doit etre la decomposition en nombres premiers du pgcd ?" }}{PARA 14 "" 0 "" {TEXT -1 27 "b) calculez le r\351sultat de " }{XPPEDIT 18 0 "773^3570;" "6#*$\"$t(\"%qN" }{TEXT -1 15 " mod 3 571 ; de " }{XPPEDIT 18 0 "123^3570;" "6#*$\"$B\"\"%qN" }{TEXT -1 76 " mod 3571. Choisissez un nombre n entre 1 et 3570. calculez le resulta t de " }{XPPEDIT 18 0 "n^3570;" "6#*$%\"nG\"%qN" }{TEXT -1 41 "mod 35 71. Cela vous semble-t-il logique ?" }}{PARA 14 "" 0 "" {TEXT -1 38 "c ) Quel est le 500\350me nombre premier ?" }}{PARA 14 "" 0 "" {TEXT -1 122 "d) Donnez la d\351composition en facteurs premiers de 200! D'apr \350s vous par combien de z\351ros le nombre 200! se termine-t-il ?" } }}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 27 " 3. Caculs sur les polynomes" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 130 "N ous allons pouvoir commencer \340 travailler sur les expressions symbo liques. Prennons la plus simple d'entre-elles : les polynomes." }} {PARA 0 "" 0 "" {TEXT -1 32 "Donnons le nom \"PP\" au polynome " } {XPPEDIT 18 0 "3*x^2+4*x+7;" "6#,(*&\"\"$\"\"\"*$%\"xG\"\"#F&F&*&\"\"% F&F(F&F&\"\"(F&" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "PP:=3*x^2+4*x +7;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 60 "Pour connaitre le carr\351 de ce polynome , il suffit de taper :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "PP ^2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Donnons le \+ nom 'QQ' au polynome " }{XPPEDIT 18 0 "x^3-1;" "6#,&*$%\"xG\"\"$\"\"\" \"\"\"!\"\"" }{TEXT -1 38 " et faisons le quotient de PP par QQ :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "QQ:= x^3-1;\nPP/QQ;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "On peut bien entendu ev aluer la valeur d'un polynome pour un x donn\351, grace \340 la comman de " }{TEXT 279 17 "eval(... , x=...)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eval(PP,x=2);\neval(PP/QQ, x=-1);" }}{PARA 11 "" 1 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "De meme on peut developper, factoriser, simplifier et ordonn\351 des polynomes, grace aux comamndes " }{TEXT 280 54 "expand(...), factor(...), collect(... ), simplify(...)" }{TEXT -1 4 " et " }{TEXT 281 10 "sort(...)." } {TEXT -1 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 " " {TEXT -1 27 "3.1 La commande factor(...)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "factor(21*x^3+151 *x^2+324*x+180);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "factor(x^2-4);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "factor(x^2-2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "factor(x^2-2*x+2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(x^2+x+1);" }{TEXT -1 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "L a commande " }{TEXT 282 11 "factor(...)" }{TEXT -1 72 " peut etre \351 galement utilis\351e pour des polynomes \340 plusieurs variables :" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(x^3-y^3);" }}} {EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 28 "3. 2 La commande collect(...)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 283 12 "collect(...) " }{TEXT -1 75 " permet de grouper les termes d'une expression suivant une variable donn\351e." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "collect(a*x^3 +y*x-(x^2+1)*(y-2)+4 , x);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 40 "collect(a*x^3 +y*x-(x^2+1)*(y-2)+4 , y);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 113 "On peut bien sur faire cette \"collection\" suivant plus ieurs variables, avec le respect de l'ordre des variables :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "collect(a*x^3 +y*x-(x^2+1)*( y-2)+4,[x,y]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "collect(a*x^3 +y*x-(x^2+1)*(y-2)+4,[y,x]);" }{TEXT -1 0 "" }}} {EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 44 "3. 3 Autres commandes Maple sur les polynomes" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 284 12 "normal(...) " }{TEXT -1 65 "permet de mettree une fraction au \+ meme d\351nominateur. La commande " }{TEXT 285 14 "simplify(...) " } {TEXT -1 125 "permet de simplifier le r\351sultat. Attention cependant \340 la commande simplify, elle ne donne aps toujorus le r\351sultat \+ voulu..." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "1/(1-x+2*x^2)+2*x/(1-x+2*x^2)+3*x^2/(1-x+2*x^2)-2*x^3 /(1-x+2*x^2);\nnormal(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "(x^5-3*x^3-x^4+2*x+4)/(x^4+x-2*x^3-2);\nsimplify(%);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 286 9 "sort(...)" }{TEXT -1 86 " cla sse les ccoeficients d'un polynomes suivant les valeur croissantes des puissances." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "poly:=x+x^2 -x^3+7-x^6+x^22;\nsort(poly);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 287 14 "coef(... , x^n)" }{TEXT -1 52 " permt d'obtenir le coefficient du terme de degr \351 n." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "coeff(poly,x^3); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "coeff(poly,x^15);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 289 12 "degree(...) " }{TEXT -1 53 "donne le degr \351 d'un polynome, tandis que la comamnde " }{TEXT 288 11 "lcoef(...) " }{TEXT -1 41 "donne le coeficient de son premier terme." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "PP:=4*x^5 -2*x^4 + 3*x^3 -3*x^2 +2* x +1;\ndegree(PP);\nlcoeff(PP);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 290 11 "Exercice 3." }}{PARA 14 "" 0 "" {TEXT -1 44 "a) Factorisez les deux polynomes suivants : " }{XPPEDIT 18 0 "p[1] = x^4-1;" "6#/&%\"pG6#\"\"\",&*$%\"xG\"\"%\"\"\"\"\"\"!\"\" " }{TEXT -1 4 " et " }{XPPEDIT 18 0 "p[2] = x^3+x^2-5*x-5;" "6#/&%\"pG 6#\"\"#,**$%\"xG\"\"$\"\"\"*$F*\"\"#F,*&\"\"&F,F*F,!\"\"\"\"&F1" }} {PARA 14 "" 0 "" {TEXT -1 14 " Que vaut " }{XPPEDIT 18 0 "p[1]/p[2 ];" "6#*&&%\"pG6#\"\"\"\"\"\"&F%6#\"\"#!\"\"" }{TEXT -1 2 " ?" }} {PARA 14 "" 0 "" {TEXT -1 39 "b) Donnez le nom 'poly' \340 l'expressio n " }{XPPEDIT 18 0 "(x^2-a)*(x*y+b)*(x^4-y^4)*(3*x+z)*(z-x)" "6#*,,&*$ %\"xG\"\"#\"\"\"%\"aG!\"\"F(,&*&F&F(%\"yGF(F(%\"bGF(F(,&*$F&\"\"%F(*$F -\"\"%F*F(,&*&\"\"$F(F&F(F(%\"zGF(F(,&F7F(F&F*F(" }{TEXT -1 48 ". Deve loppez, simplifiez et ordonnez ce polynome" }}{PARA 14 "" 0 "" {TEXT -1 30 " Donnez le coefficient de " }{XPPEDIT 18 0 "x^5;" "6#*$%\"x G\"\"&" }{TEXT -1 30 " pour l'expression pr\351cedente." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 13 "4. Equati ons." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Maple sait aussi r\351soudre presque n'importe quelle \351quat ion. Les commandes pour r\351soudre des \351quatiosn sont " }{TEXT 294 10 "solve(...)" }{TEXT -1 4 " et " }{TEXT 297 11 "fsolve(...)" } {TEXT -1 1 "." }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 14 "4.1 Equations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "eqn1 := x^2 - 4 = 0;" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "(Notez que l'expr ession " }{TEXT 298 4 "eqn1" }{TEXT -1 63 " est definie comme une \351 quation et non pas comme une variable.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(eqn1,x);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Avec cette m\351thode on vaoit juste une liste de n ombre, avec la suivant, on peut identifier la variable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(eqn1,\{x\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "On peut \+ \351galement obtenir les solutions g\351n\351rales pour les polynomes \+ du second degr\351." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eqn2 :=a*x^2+b*x+c=0;\nsolve(eqn2,\{x\});" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "Si l'ion se sp ecifie pas quel est la variable, le r\351sultat donn\351 par Maple peu t-etre surprennant...." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s olve(eqn2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 37 "De meme pour les equations cubiques." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve(x^3-1=0,\{x\});\nsolv e(eqn3,\{x\});" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 24 "4.2 Syst\350mes d'\351quations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 31 "solve(\{x+2*y=3,y+1/x=1\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Et en donnant un niom au \+ systeme :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "sys1:=\{x+2*y= 3,y+1/x=1\};\nsolve(sys1,\{x,y\});" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "On peut verifier q ue la solution donn\351e par " }{TEXT 295 5 "Maple" }{TEXT -1 15 " est la bonne :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "eval(eqns,so ln[1]);\neval(eqns,soln[2]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Voici un autre syst\350 me :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "sys2 := solve(\{x^2 +y=1,x^2-y^2=2\},\{x,y\});" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "La r\351ponse n'est que partielle, pour obtenir toutes le s valeurs, on utilie la commande " }{TEXT 296 14 "allvalues(...)" } {TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "allvalues( sys2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Let us s olve a system of equations, and then give a name to the solutions list ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "On peut forcer Maple pour qu'il donne une valeur pr\351cise \340 u n nom donn\351, \340 l'aide de la commande " }{TEXT 299 11 "assign(... )" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sys3:= \{u+v=1,2*u+v=3\};\nsol3:=solve(sys3,\{u,v\});" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "On note que u et v sont encore con sid\351r\351 par Maple comme des variable, sans valeur precise." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "u,v;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Si on veut donner \340 u et v les \+ valeurs solution du systeme precedent, on fait comme suit :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "assign(sol3);\nu,v;\nsys3;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Pour redonner le statut de variable \340 u et v on utilise la commande " }{TEXT 300 13 "unassign(...)" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "unassign('u','v');\nu,v;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "(Note: la comande " }{TEXT 301 7 "restart" }{TEXT -1 65 " permet de r\351initialiser Maple, ce qui peut etre utile, parfois.)" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 24 "4.3 Solutions num\351riques" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 303 11 "fsolv e(...)" }{TEXT -1 46 " permet d'obtenir des solution num\351riques. le " }{TEXT 305 1 "f" }{TEXT -1 4 " de " }{TEXT 304 11 "fsolve(...)" } {TEXT -1 48 " est l\340 pour 'floating', comme dans la commande " } {TEXT 306 10 "evalf(...)" }{TEXT -1 39 " que nous avons vu al semaine \+ derni\350re." }}{PARA 0 "" 0 "" {TEXT -1 19 "Pour une \351quation, " } {TEXT 308 11 "fsolve(...)" }{TEXT -1 74 " donnera bien souvent une seu le solution. Pour les polynomes, par d\351faut, " }{TEXT 309 11 "fsolv e(...)" }{TEXT -1 28 " donnera toutes les racines " }{TEXT 310 7 "r \351elles" }{TEXT -1 58 ". Pour les racines complex, il faudra utilise r la comande " }{TEXT 307 14 "allvalues(...)" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "p oly1:=3*x^4-16*x^3-3*x^2+13*x+16;\nfsolve(poly,x);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "poly2:=23*x^5+105*x^4-10*x^2 +17*x;\nfsolve(\{poly\},\{x\});" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 311 11 "fsolve(...)" } {TEXT -1 117 " a beaucoup d'option (regardez l'aide sur cette commande ). On peut specifier dans quel interval on veut laz solution." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "poly3:=3*x^4-16*x^3-3*x^2+13 *x+16;\nfsolve(poly2,x,4..8);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "grace \340 l'option " } {TEXT 312 7 "complex" }{TEXT -1 63 ", on peut sp\351cifier \340 fsolve de donner les solutions complexes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "q := x^4 +7*x^3 + 2*x^2 -4*x + 1;\nfsolve(q, x, compl ex);" }{TEXT -1 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 45 "4.4 Les commandes isolve(...) et msolve(...)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 313 11 "isolve(...)" }{TEXT -1 55 " permet de do nenr des solutions enti\350res d'une \351quation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "isolve(\{5*x-3*y=4\});" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 314 14 "msolv e( .., m)" }{TEXT -1 72 " permet de donner les solutions d'une \351qua tion modulo un certain entier " }{TEXT 315 1 "m" }{TEXT -1 1 "." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "msolve(\{x+7*y=1,3*x+2*y=2\} ,17);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 302 10 "Exercice 4" }}{PARA 14 "" 0 "" {TEXT -1 95 "a) Donnez le s solutions g\351n\351rales d'un polynome du 3e degr\351 (ie: Quelles \+ sont les solutions de " }{XPPEDIT 18 0 "p = a*x^3+b*x^2+c*x+d;" "6#/% \"pG,**&%\"aG\"\"\"*$%\"xG\"\"$F(F(*&%\"bGF(*$F*\"\"#F(F(*&%\"cGF(F*F( F(%\"dGF(" }{TEXT -1 3 " ?)" }}{PARA 14 "" 0 "" {TEXT -1 52 "b) Determ inez les solutions de l'equation suivante: " }{XPPEDIT 18 0 "exp(x)-3* x = 0;" "6#/,&-%$expG6#%\"xG\"\"\"*&\"\"$F)F(F)!\"\"\"\"!" }{TEXT -1 1 "." }}{PARA 14 "" 0 "" {TEXT -1 39 "c) Resoudre le syst\350me suivan t :\n " }{XPPEDIT 18 0 "x+2*y+3*z+4*t+10 = 41" "6#/,,%\"xG\"\"\"* &\"\"#F&%\"yGF&F&*&\"\"$F&%\"zGF&F&*&\"\"%F&%\"tGF&F&\"#5F&\"#T" } {TEXT -1 7 "\n " }{XPPEDIT 18 0 "8*x+4*z+3*t+4 = 11;" "6#/,**&\" \")\"\"\"%\"xGF'F'*&\"\"%F'%\"zGF'F'*&\"\"$F'%\"tGF'F'\"\"%F'\"#6" } {TEXT -1 7 "\n " }{XPPEDIT 18 0 "x+y+z+t+2 = 9;" "6#/,,%\"xG\"\" \"%\"yGF&%\"zGF&%\"tGF&\"\"#F&\"\"*" }{TEXT -1 7 "\n " }{XPPEDIT 18 0 "3*y+4*z-8*t+4 = 125;" "6#/,**&\"\"$\"\"\"%\"yGF'F'*&\"\"%F'%\"zG F'F'*&\"\")F'%\"tGF'!\"\"\"\"%F'\"$D\"" }{TEXT -1 6 " " }}{PARA 14 "" 0 "" {TEXT -1 35 "Puis, r\351soudre le syst\350me suivant :" }} {PARA 14 "" 0 "" {TEXT -1 6 " " }{XPPEDIT 18 0 "x+2*y+3*z+4*t+10 \+ = 41" "6#/,,%\"xG\"\"\"*&\"\"#F&%\"yGF&F&*&\"\"$F&%\"zGF&F&*&\"\"%F&% \"tGF&F&\"#5F&\"#T" }{TEXT -1 7 "\n " }{XPPEDIT 18 0 "8*x+4*z+3*t +4 = 11;" "6#/,**&\"\")\"\"\"%\"xGF'F'*&\"\"%F'%\"zGF'F'*&\"\"$F'%\"tG F'F'\"\"%F'\"#6" }{TEXT -1 7 "\n " }{XPPEDIT 18 0 "x+y+z+t+2 = 9; " "6#/,,%\"xG\"\"\"%\"yGF&%\"zGF&%\"tGF&\"\"#F&\"\"*" }}{PARA 14 "" 0 "" {TEXT -1 32 "d) R\351soudre le systeme suivant :" }}{PARA 14 "" 0 " " {TEXT -1 6 " " }{XPPEDIT 18 0 "x+y+2*z = 2;" "6#/,(%\"xG\"\"\"% \"yGF&*&\"\"#F&%\"zGF&F&\"\"#" }{TEXT -1 13 " \n " } {XPPEDIT 18 0 "2*x+3*y+z = 4;" "6#/,(*&\"\"#\"\"\"%\"xG\"\"\"F)*&\"\"$ F)%\"yGF)F)%\"zGF)\"\"%" }{TEXT -1 7 "\n " }{XPPEDIT 18 0 "x-y+5* z = 7;" "6#/,(%\"xG\"\"\"%\"yG!\"\"*&\"\"&F&%\"zGF&F&\"\"(" }}{PARA 14 "" 0 "" {TEXT -1 52 "e) Trouvez toutes les solutions du systeme sui vant :" }}{PARA 14 "" 0 "" {TEXT -1 6 " " }{XPPEDIT 18 0 "x^2+y^2 = 3;" "6#/,&*$%\"xG\"\"#\"\"\"*$%\"yG\"\"#F(\"\"$" }}{PARA 14 "" 0 " " {TEXT -1 6 " " }{XPPEDIT 18 0 "x^2+2*y^2 = 3." "6#/,&*$%\"xG\" \"#\"\"\"*&\"\"#F(*$%\"yG\"\"#F(F($\"\"$\"\"!" }}{PARA 14 "" 0 "" {TEXT -1 72 "f) Trouvez une solution approximative strictement positiv e \340 l'\351quation " }{XPPEDIT 18 0 "tan(x)-x = 0;" "6#/,&-%$tanG6#% \"xG\"\"\"F(!\"\"\"\"!" }{TEXT -1 1 "." }}{PARA 14 "" 0 "" {TEXT -1 52 "g) Trouvez une solution approximative de l'\351quation " } {XPPEDIT 18 0 "tan(sin(x)) = 1;" "6#/-%$tanG6#-%$sinG6#%\"xG\"\"\"" } {TEXT -1 7 " entre " }{XPPEDIT 18 0 "-Pi;" "6#,$%#PiG!\"\"" }{TEXT -1 4 " et " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }}{PARA 14 "" 0 "" {TEXT -1 0 "" }}}}{MARK "137 7 0" 3 }{VIEWOPTS 1 1 0 1 1 1803 }