已知x^2-y^2=4xy,求(x^4+y^4)/(xy)^2的值

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已知x^2-y^2=4xy,求(x^4+y^4)/(xy)^2的值
已知x^2-y^2=4xy,求(x^4+y^4)/(xy)^2的值

已知x^2-y^2=4xy,求(x^4+y^4)/(xy)^2的值
(x^4+y^4)/(xy)^2
=(x^4+y^4-2x^2y^2+2(xy)^2)/(xy)^2
=((x^2-y^2)^2/(xy)^2+2
=(4xy)^2/(xy)^2+2
=16+2
=18

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