计算:(1/x-y-1/x+y)/2y/x^2-2xy+y^2,x=1+根号2,y=1-根号2
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计算:(1/x-y-1/x+y)/2y/x^2-2xy+y^2,x=1+根号2,y=1-根号2
![计算:(1/x-y-1/x+y)/2y/x^2-2xy+y^2,x=1+根号2,y=1-根号2](/uploads/image/z/19498199-23-9.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%281%2Fx-y-1%2Fx%2By%29%2F2y%2Fx%5E2-2xy%2By%5E2%2Cx%3D1%2B%E6%A0%B9%E5%8F%B72%2Cy%3D1-%E6%A0%B9%E5%8F%B72)
[1/(x-y)-1/(x+y)]/[2y/(x^2-2xy+y^2)]
={[(x+y)-(x-y)]/[(x+y)(x-y)]}*(x^2-2xy+y^2)/2y
={2y/[(x+y)(x-y)]}*{(x-y)^2/2y}
=(x-y)/(x+y)
x=1+根号2,y=1-根号2,代入
原式=【(1+根号2)-(1-根号2)】/【(1+根号2)+(1-根号2)】
=(2根号2)/2
=根号2
={[(x+y)-(x-y)]/[(x+y)(x-y)]}*(x^2-2xy+y^2)/2y
={2y/[(x+y)(x-y)]}*{(x-y)^2/2y}
=(x-y)/(x+y)
x=1+根号2,y=1-根号2,代入
原式=【(1+根号2)-(1-根号2)】/【(1+根号2)+(1-根号2)】
=(2根号2)/2
=根号2
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