已知x=1/y,则(x-1/x)(y-1/y)等于A.2X^2 B.2Y^2 C.X^2+Y^2 D.2-X^2-Y^2
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已知x=1/y,则(x-1/x)(y-1/y)等于A.2X^2 B.2Y^2 C.X^2+Y^2 D.2-X^2-Y^2
已知x=1/y,则(x-1/x)(y-1/y)等于
A.2X^2 B.2Y^2 C.X^2+Y^2 D.2-X^2-Y^2
已知x=1/y,则(x-1/x)(y-1/y)等于A.2X^2 B.2Y^2 C.X^2+Y^2 D.2-X^2-Y^2
(x-1/x)(y-1/y)
=xy-x/y-y/x-1/xy
∵x=1/y
∴xy-x/y-y/x-1/xy
=y×1/y--x/y-y/x-1/(y×1/y)
=2-(x²+y²)/xy
=2-(x²+y²)/(y×1/y)
=2-x²-y²
选D.
关于您的问题,答案为D.2-X^2-Y^2
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D.2-X^2-Y^2
x=1/y
xy=1
(x-1/x)(y-1/y)
=xy - x/y - y/x +1/xy
=1-(x/y +y/x)+1
=2-(x^2 +y^2)/xy
=2-x^2 -y^2
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