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

Найдите |x|+|y|

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