Question

(x-y)的平方=8,x的平方+y的平方=10,求x的四次方+y的四次方的值

Answer 1

(x-y)^2=8

x^2+y^2-2xy=8 .(1)

x^2+y^2=10 .(2)

(2)-(1)得：

2xy=2

xy=1

x^4+y^4

=x^4+y^4+2x^2y^2-2x^2y^2

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

=10^2-2*1^2

=100-2

=98