已知(x-y)²=10 ,(x+y)²=2,求x⁴+y⁴的值

题目

已知(x-y)²=10 ,(x+y)²=2,求x⁴+y⁴的值
如题

答案

(x-y)^2=10
x^2-2xy+y^2=10 (1)
(x+y)^2=2
x^2+2xy+y^2=2 (2)
(1)+(2)
2(x^2+y^2)=12
x^2+y^2=6
xy=-2
x^4+y^4
=(x^2+y^2)^2-2(xy)^2
=6^2-2*(-2)^2
=36-8
=28