Question

Proszę o pomoc x+y=1 x^2+y^2=8 x^4+y^4=?

Answer 1

x + y = 1

 

x^2 + y^2 = 8

(x + y)^2 - 2xy = 8

1^2 - 2xy = 8

-2xy = 8 - 1

-2xy = 7

xy = -3,5

 

 

x^4 + y^4 = (x^2 + y^2)^2 - 2x^2y^2 = 8^2 - 2(xy)^2 = 64 - 2 * (-3,5)^2 = 64 - 2 * 12,25 = 64 - 24,5 = 39,5