已知(x-y)²=8,xy=2,x⁴+y⁴=?
问题描述：
已知(x-y)²=8,xy=2,x⁴+y⁴=?
答
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