Maple tizimida tenglama va tengsizliklarni, tenglama va tengsizliklar sistemasini yechish

Trigonometrik tenglamalarni yechish
solve buyrug’i trigonometrik tenglamalarni yechish uchun qo`llanilib, [0;2] intervaldagi bosh yechimni ko`rsatadi To`la yechimni ko`rsatish uchun _EnvAllSolutions:=true davomiy buyrug’i qo`llaniladi.Masalan:

• _EnvAllSolutions:=true:
• solve(sin(x)=cos(x),x);

4
1   _ Z ~
Maple da  _Z~ belgisi butun tipning o`zgarmasini aniqlaydi, bu berilgan tenglama yechimi uchun x :  / 4  n , n – butun son.
Misol 1. Tenglamaning (0;2) oraliqqa tegishli yechimlarini toping. cos x  
2
2
Maple dasturida yechish:

• _EnvAllSolutions:=true:
• solve(cos(x)=-sqrt(2)/2,x);

3 p - 3 p _B1~ + 2 p _Z2~
4 2
Misol 2. sin 2x  cos x  sin x2 tenglamaning [0;2] kesmada nechta ildizi bor?
Maple dasturida yechish:

• _EnvAllSolutions:=true:
• solve(sin(2*x)=(cos(x)-sin(x))^2);

1 p + p _Z3~, 5 p + p _Z3~
12 12

Transendent tenglamalarni yechish
Transendent tenglamani yechishda, yechim aniq ko`rinishda bo`lishi uchun
_EnvExplicit:=true buyrug’ini ifodalash kerak.
solve buyrug’idan avval

• eq:={ 7*3^x-3*2^(z+y-x+2)=15, 2*3^(x+1)+

3*2^(z+y-x)=66, ln(x+y+z)-3*ln(x)-ln(y*z)=-ln(4) }:

• _EnvExplicit:=true:

• s:=solve(eq,{x,y,z}):
• simplify(s[1]);simplify(s[2]);

{x=2, y=3, z=1}, {x=2, y=1, z=3}
Quyida keltirilgan ko’rsatkichli tenglama va tengsizliklarning yechimi Maple muhitida topilgan.
Misol 1. Tenglamani yeching. 4x4  0,5
Maple dasturida yechish:

• eq:={4^(x-4)=0.5};

eq := {4 (x - 4) = 0.5 }

• _EnvExplicit:=true:
• s:=solve(eq,{x});

s := {x = 3.500000000}
Javob: x = 3,5

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