已知x²+y²-2x+4y+5=0,求X^4-y^4/2x^2+xy-y²·2x-y/xy-y^2÷(x^2+y^2)^2的值
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![已知x²+y²-2x+4y+5=0,求X^4-y^4/2x^2+xy-y²·2x-y/xy-y^2÷(x^2+y^2)^2的值](/uploads/image/z/2517229-37-9.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B%2By%26%23178%3B-2x%2B4y%2B5%3D0%2C%E6%B1%82X%5E4-y%5E4%2F2x%5E2%2Bxy-y%26%23178%3B%C2%B72x-y%2Fxy-y%5E2%C3%B7%28x%5E2%2By%5E2%29%5E2%E7%9A%84%E5%80%BC)
已知x²+y²-2x+4y+5=0,求X^4-y^4/2x^2+xy-y²·2x-y/xy-y^2÷(x^2+y^2)^2的值
已知x²+y²-2x+4y+5=0,求X^4-y^4/2x^2+xy-y²·2x-y/xy-y^2÷(x^2+y^2)^2的值
已知x²+y²-2x+4y+5=0,求X^4-y^4/2x^2+xy-y²·2x-y/xy-y^2÷(x^2+y^2)^2的值
x²+y²-2x+4y+5=0
配方:(x-1)²+(y+2)²=0
所以只有x-1=0且y+2=0
∴x=1,y=-2
∴(X^4-y^4)/(2x^2+xy-y²)·[(2x-y)/(xy-y^2)]÷(x^2+y^2)^2
=(x²+y²)(x²-y²)/[(2x-y)(x+y)]× (2x-y)/[y(x-y)] ÷(x²+y²)²
=(x²-y²)/(x+y)× 1/[y(x-y)] ÷(x²+y²)
=(x+y)(x-y)/(x+y)×1/[y(x-y)]÷(x²+y²)
=1/y÷(x²+y²)
=1/[y(x²+y²)]
=1/[-2(1+4)]
=-1/10