Question

已知(x-y)²=8,xy=2,x⁴+y⁴=?

Answer 1

x^4+y^4=(x^2+y^2)^2-2x^2*y^2=(x^2+y^2-2xy+2xy)^2-2x^2*y^2

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

=(8+2*2)^2-2*2^2

=144-8

=136