Помогите решить систему! x^2-xy+y^2=7 3x^2-4xy+3y^2=15. Created by YuliaOv2002. algebra-ru

Помогите решить систему! x^2-xy+y^2=7 3x^2-4xy+3y^2=15...

YuliaOv2002 @YuliaOv2002

July 2022 2 5 Report

Помогите решить систему!
x^2-xy+y^2=7
3x^2-4xy+3y^2=15

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N777A Складываем уравнения,умножив первое на -4:
-x^2-y^2=-13
Складываем уравнения, умножив первое на -3:
-xy=-6
Выражаем y=6/x
Подставляем в первое:
-x^2-(6/x)^2=-13
-x^2 - (6/x)^2 = -36/x^2 - x^2:
-36/x^2 - x^2 = -13
(-x^4 - 36)/x^2 = -13
-x^4 - 36 = -13 x^2
-x^4 + 13 x^2 - 36 = 0
y=x^2
-y^2 + 13 y - 36 = 0
-((y - 9) (y - 4)) = 0
(y - 9) (y - 4) = 0
y - 9 = 0, y - 4=0
y = 9, y = 4
x^2 = 9
x = 3, x = -3
x^2 = 4
x = 2, x = -2
Ответ: x=3, y=2, x=-3, y=-2.

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