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Вправа 583 алгебра Істер гдз 9 клас

ГДЗ 9 клас алгебра Істер
Задача №583
Умова:
Знайдіть розв'язки системи рівнянь:
1.

{x−y=2x2+y2=34 \left\{\begin{array}{l} x-y=2 \\ x^2+y^2=34 \end{array}\right.

2.

{x+y=9x2−y2=9 \left\{\begin{array}{l} x+y=9 \\ x^2-y^2=9 \end{array}\right.


{x−y=2,x2+y2=34.{x=y+2,(y+2)2+y2=34.{x=y+2,y2+4y+4+y2=34.{x=y+2,2y2+4y−30=0.{x=y+2,y2+2y−15=0.{x=y+2,(y−3)(y+5)=0.{y=3,x=3+2=5y=−5,x=−5+2=−3. \begin{aligned} & \left\{\begin{array}{l} x-y=2, \\ x^2+y^2=34 . \end{array}\right. \\ & \left\{\begin{array}{l} x=y+2, \\ (y+2)^2+y^2=34 . \end{array}\right. \\ & \left\{\begin{array}{l} x=y+2, \\ y^2+4 y+4+y^2=34 . \end{array}\right. \\ & \left\{\begin{array}{l} x=y+2, \\ 2 y^2+4 y-30=0 . \end{array}\right. \\ & \left\{\begin{array}{l} x=y+2, \\ y^2+2 y-15=0 . \end{array}\right. \\ & \left\{\begin{array}{l} x=y+2, \\ (y-3)(y+5)=0 . \end{array}\right. \\ & \left\{\begin{array}{l} y=3, \quad x=3+2=5 \\ y=-5, \quad x=-5+2=-3 . \end{array}\right. \end{aligned}
Відповідь:

(5,3) або (−3,−5). {x+y=9,x2−y2=9.{x+y=9(x−y)(x+y)=9.{x+y=9(x−y)(9)=9.{x+y=9x−y=1{x=9+12=5,y=9−12=4. \begin{aligned} & (5,3) \text { або }(-3,-5) \text {. } \\ & \left\{\begin{array}{l} x+y=9, \\ x^2-y^2=9 . \end{array}\right. \\ & \left\{\begin{array}{l} x+y=9 \\ (x-y)(x+y)=9 . \end{array}\right. \\ & \left\{\begin{array}{l} x+y=9 \\ (x-y)(9)=9 . \end{array}\right. \\ & \left\{\begin{array}{l} x+y=9 \\ x-y=1 \end{array}\right. \\ & \left\{\begin{array}{l} x=\frac{9+1}{2}=5, \\ y=\frac{9-1}{2}=4 . \end{array}\right. \end{aligned}


Відповідь:

(5,4) (5,4)