(1)已知x-y=6,xy=4,求xy^-1+x^-1y的值； (2)已知x^2+y^2=3xy且xy≠0,求x^2y^-2+x^-2y^2的值.

题目

(1)已知x-y=6,xy=4,求xy^-1+x^-1y的值； (2)已知x^2+y^2=3xy且xy≠0,求x^2y^-2+x^-2y^2的值.

答案

∵x-y=6,xy=4∴(x-y)²=36∴x²-2xy+y²=36∴x²+y²=36+2×4=44两边除以xyx/y+y/x=44/4=11∴xy^-1+x^-1y=112x^2+y^2=3xy两边除以xyx/y+y/x=3两边平方（x/y+y/x)²=9x²/y²+y²...