(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.

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(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.(1)已知x-y=6,xy=4,求xy^-1+x^-1y

(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.
(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.

(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.
∵x-y=6,xy=4
∴(x-y)²=36
∴x²-2xy+y²=36
∴x²+y²=36+2×4=44
两边除以xy
x/y+y/x=44/4=11
∴xy^-1+x^-1y=11
2
x^2+y^2=3xy
两边除以xy
x/y+y/x=3
两边平方
(x/y+y/x)²=9
x²/y²+y²/2²+2=9
∴x^2y^-2+x^-2y^2=7