maple tizimida tenglama va tengsizliklarni, tenglama va tengsizliklar sistemasini yechish

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1348674565_2767.doc a c b - - x x 8 x 8.099999999 12 143 99 63 35 15 3 = + + + + + x x x x x x 26 0 2 5 , 2 2 3 2 4 2 3 = + - + + - x x x 4. a a x , : - = a - a 0 2 2000 1998 2 = + - x x 1 , 1 999 x := 1 , 1 999 1 1 999 1 x 2 x 0 6 2 3 2 = - - x x x := 1 3 + 1 3 19 , 1 3 - 1 3 19 1 3 + 1 3 19 1 3 - 1 3 19 2 3 2 3 19 2 2 5 5 , 5 1 a a y a a x + - = + + = …

( 4 3 3 ) 1 ( 10 ) 1 ( 2 { } 6 , 6 + - - 6 25 ) 1 5 )( 1 5 ( ) 1 6 )( 3 2 ( 12 2 2 x x x x x x x x þ ý ü î í ì £ = ko`rinishida hosil qilinadi. tenglama ma’lumot sifatida talqin qilinganligi tufayli, uning ustida turli xil amallar bajarish mumkin. masalan, chap va o`ng qismlarini ajratib olib, ular ustida oddiy ifodalar uchun qo`llanilgan barcha komandalarni bajarish mumkin. tenglama va tengsizliklar yoki ularning sistemalarini analitik yechish uchun: a) solve( , ); b) solve({ , ,...}, { , ,...); komandalari qo`llaniladi. a) ko`rinishdagi komanda bitta tenglamani, b) ko`rinishdagi komanda esa tenglamalar sistemasini yechadi. bitta tenglamani yechish komandasining natijasi yechim yoki yechimlar ketma-ketligi bo`ladi. tenglamalar sistemasini yechadigan komandaning natijasi yechimlar to`plami ketma-ketligi bo`ladi. agarda komandada o`zgaruvchi(o`zgaruvchilar) ko`rsatilmasa, u holda komanda tenglamada qatnashgan …

$lve(1998*x^2-2000*x+2=0,x); > x:=solve(1998*x^2-2000*x+2=0,x); > x[1]; > x[2]; misol 2. va sonlari tenglamaning ildizlari bo’lsa, ildizlari yig’indisi va ayirmasini toping. > x:=solve(3*x^2-2*x-6=0,x); > x[1]; > x[2]; > x[1]+x[2]; > x[1]-x[2]; tenglamalar sistemasini yechish tenglamalar sistemasi solve({eq1,eq2,…},{x1,x2,…}),buyrug’i yordamida yechiladi, faqat aylana qavslar ichidagi 1- figurali qavs ichida tenglamalar, ikkinchi figurali qavs ichida esa tenglamaning o`zgaruvchilari kiritiladi. agar sizga tenglamaning yechimlari bilan bog’liq ravishda keyingi hisoblashlar kerak bo`lsa, solve komandasi name ning qandaydir nomini ifodalaydi. so`ngra assign(name) buyrug’i uni to`ldiradi. shundan keyin yechimlar ustida matematik amallar bajarish mumkin. masalan: > s:=solve({a*x-y=1,5*x+a*y=1},{x,y}); s:={ } > assign(s); simplify(x-y); misol 1. tenglamalar sistemasini yeching maple dasturida yechish: > s:=solve({(x+y)/2-2*y/3=5/2, 3*x/2+2*y=0},{x,y}); javob: (4, -3) misol 2. (x,y) sonlar jufti sistemaning yechimi bo’lsa, x – y ni toping. maple dasturida yechish: > s:=solve({2*x-y=5,3*x+2*y=4},{x,y}); > assign(s);simplify(x-y); javob: x – y =3 misol 3. agar bo’lsa, x+y+z nimaga teng. maple dasturida yechish: > s:=solve({3*x+y=45, z+3*y=-15, 3*z+x=6},{x,y,z}); s := {z = …$

$=2,5 misol 4. tenglamalar sistemasini yeching. maple dasturida yechish: > s:=solve({y+4=2, (x^2)*y=-2},{x,y}); > s[1]; > s[2]; javob: (-1; -2), (1; -2) misol 4. agar va bo’lsa, ning qiymati qancha bo’ladi? maple dasturida yechish: > s:=solve({x-y=5, x*y=7},{x,y}); > assign(s); simplify(x^3*y+x*y^3); javob: =273 misol 5. agar va bo’lsa, a ning qiymati qanchaga teng? maple dasturida yechish: > k:=solve({a-b=12, (-a)*b+a^2=144}, {a,b}); > assign(k); simplify(a); javob: a=12 misol 6. agar va bo’lsa, ning qiymatini toping. maple dasturida yechish: > k:=solve({x^2-4*x*y+y^2=4-2*x*y, x+y=12}, {x,y}); > assign(k); simplify(x*y); javob: =35 misol 7. va , maple dasturida yechish: > t:=solve({b+a=18, a^2+b^2=170}, {a,b}); · assign(t); simplify(a*b); javob: misol 8. tenglamalar sistemasidan x ni toping. maple dasturida yechish: > s:=solve({x*y/(x+y)=10/7, y*z/(y+z)=40/13, z*x/(x+z)=5/8}, {x,y,z}); > assign(s); simplify(x); javob: tenglamalarning sonli yechimi tenglamani sonli yechishda, berilgan transcendent tenglama analitik yechim bermasa, maxsus fsolve(eq,x) buyrug’idan foydalaniladi. parametr xuddi solve dagi kabi ko`rsatiladi. masalan: > x:=fsolve(cos(x)=x,x); x:=.7390851332 agar komanda berilgan tenglama(tenglamalar sistemasi)ning yechimini aniqlay …$

$ish oralig’i bo`lgan interval ko`rinishida beriladigan tengsizlikning yechimi yarim o`qlarda bo`lsa, u/h realrange(–(, open(a)), ya’ni x((–(, a), а – ixtiyoriy son. open so`zi interval ochiq chegara degan ma’noni anglatadi. agar ushbu so`z bo`lmasa, tenglamalr to`plamida bu interval yopiqligini anglatadi.masalan: > s:=solve(sqrt(x+3) convert(s,radical); realrange agar siz x((a, b) ko`rinishda ko`rishni istamasangiz, berilagan o`zgaruvchini a solve(1-1/2*ln(x)>2,{x}); tengsizliklar sistemasini yechish solve buyrug’i yordamida tengsizliklar sistemasini ham yechish mumkin. masalan: > solve({x+y>=2,x-2*y =0,x-2*y>=1},{x,y}); misol 1. tengsizliklar sistemasi nechta butun yechimga ega? maple dasturida yechish: > solve({3+4*x>=5, 2*x-3*(x-1)>-1},x); javob: tengsizliklar sistemasi 3 ta butun yechimga ega. misol 2. tengsizliklar sistemasini yeching. maple dasturida yechish: > solve({x*(x+1)+10>(x+1)^2+3, 3*x-4*(x-7)>=16-3*x},x); misol 3. tengsizliklar sistemasini yeching. maple dasturida yechish: > solve({(y-5)/4 solve({1256/314 solve({(x+5)/4-2*x>=0, x-(2*x-8)/5>=1-2*x},x); javob: tengsizliklar sistemasining eng katta butun yechimi 0. misol 6. tengsizliklar sistemasining butun sonlardan iborat yechimlari yig’indisini toping. maple dasturida yechish: > solve({12*x^2-(2*x-3)*(6*x+1)>x, (5*x-1)*(5*x+1)-25*x^2>=x-6},x); javob: tengsizliklar sistemasining butun sonlardan iborat yechimlari yig’indisi 15 ga teng. …$

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1348674565_2767.doc a c b - - x x 8 x 8.099999999 12 143 99 63 35 15 3 = + + + + + x x x x x x 26 0 2 5 , 2 2 3 2 4 2 3 = + - + + - x x x 4. a a x , : - = a - a 0 2 2000 1998 2 = + - x x 1 , 1 999 x := 1 , 1 999 1 1 999 1 x 2 x 0 6 2 3 2 = - - x x x := 1 3 + 1 3 19 , 1 3 - 1 3 19 1 3 + 1 3 19 …

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