已知x^2-y^2=4xy,求(x^4+y^4)/x^2y^2的值?

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

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

x^2-y^2=4xy 两边都除以XY 则X/Y-Y/X=4 (x^4+y^4)/x^2y^2=X^2/Y^2+Y^2/X^2=(X/Y-Y/X)^2+2=4^2+2=18