已知:x²-y²=4xy,求(x的四次方+y的四次方)除以(xy)²

问题描述:

已知:x²-y²=4xy,求(x的四次方+y的四次方)除以(xy)²

x^4+y^4=(x^2-y^2)^2+2x^2y^2
(x^4+y^4)/(x^2y^2)=((x^2-y^2)^2+2x^2y^2)/(x^2y^2)
=((4xy)^2+2x^2y^2)/(x^2y^2)
=(16x^2y^2+2x^2y^2)/(x^2y^2)
=18