X^2-y^2=xy,xy不等于0 求X^2y^-2+x^-2y^2_数学解答

X^2-y^2=xy,xy不等于0 求X^2y^-2+x^-2y^2

人气：249 ℃　时间：2019-11-23 21:51:09

解答

X^2-y^2=xy
(X^2-y^2)^2=(xy)^2
X^4+y^4-2x^2y^2=x^2y^2
X^4+y^4=3x^2y^2
X^2y^-2+x^-2y^2
=X^2/y^2+y^2/x^2
=(X^4+y^4)/x^2y^2
=3x^2y^2/x^2y^2
=3