система уравнений x^2+y^2=8,xy=4 много балов даю, помогите. Created by NastyaMoore. algebra-ru

система уравнений x^2+y^2=8,xy=4 много балов даю, помогите...

NastyaMoore @NastyaMoore

July 2022 1 3 Report

система уравнений x^2+y^2=8,xy=4 много балов даю, помогите

Answers & Comments

AnonimusPro

Verified answer

X^2+2xy+y^2-2xy=8;
xy=4
(x+y)^2-8=8
(x+y)^2=16
(x+y-4)(x+y+4)=0;
имеем 2 системы:
1) x+y-4=0
xy=4;
x=4/y
4/y+y=4
y^2-4y+4=0;
(y-2)^2=0; y=2;
x=4/2=2
2) x+y+4=0
xy=4
x=4/y
4/y+y+4=0;
y^2+4y+4=0;
(y+2)^2=0;
y=-2;
x=4/-2=-2
Ответ: (2;2) и (-2;-2)

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