已知：x²-y²=4xy,求(x的四次方+y的四次方）除以（xy）²

已知：x²-y²=4xy,求(x的四次方+y的四次方）除以（xy）²
已知：x²-y²=4xy,求(x的四次方+y的四次方）除以（xy）²

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

(x的四次方+y的四次方）除以（xy）²
=[(x²-y²)²+2x²y²]/x²y²
=(16x²y²+2x²y²)/x²y²
=18