Зная что 8 (x^4+y^4)-4 (x^2+y^2)+1=0 Найдите |x|+|y|

Question

Зная что 8 (x^4+y^4)-4 (x^2+y^2)+1=0
Найдите |x|+|y|

Answer 1

8(x^4+y^4)-4(x^2+y^2)+1=0
(x^4+y^4)-(1/2)(x^2+y^2)+(1/8)=0
(x^4+y^4)-(1/2)(x^2+y^2)+(1/8)=x^4-(1/2)x^2+(1/16)+y^4-(1/2)y^2+(1/16)=
(x^2-(1/4))^2+(y^2-(1/4))^2
(x^2-(1/4))^2+(y^2-(1/4))^2=0⇒x^2-(1/4)=0 y^2-(1/4)⇒|x|=(1/2) |y|=(1/2)⇒
|x|+|y|=1