分数指数幂的化简求值已知x+y=12,xy=9.求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值
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分数指数幂的化简求值
已知x+y=12,xy=9.求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值
已知x+y=12,xy=9.求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值
![分数指数幂的化简求值已知x+y=12,xy=9.求(x^1/2-y^1/2)/(x^1/2+y^1/2)的值](/uploads/image/z/8356624-16-4.jpg?t=%E5%88%86%E6%95%B0%E6%8C%87%E6%95%B0%E5%B9%82%E7%9A%84%E5%8C%96%E7%AE%80%E6%B1%82%E5%80%BC%E5%B7%B2%E7%9F%A5x%2By%3D12%2Cxy%3D9.%E6%B1%82%EF%BC%88x%5E1%2F2-y%5E1%2F2%29%2F%28x%5E1%2F2%2By%5E1%2F2%29%E7%9A%84%E5%80%BC)
x+y=12
两边平方
x^2+2xy+y^2=144
x^2+y^2=144-2xy=126
(x-y)^2=x^2-2xy+y^2=108
x-y=±6√3
(x^1/2-y^1/2)/(x^1/2+y^1/2)
上下乘x^1/2-y^1/2
=(x^1/2-y^1/2)^2/(x^1/2-y^1/2)(x^1/2+y^1/2)
=[x-2(xy)^(1/2)+y]/(x-y)
=(12-2×3)/(±6√3)
=6/(±6√3)
=√3/3或-√3/3
两边平方
x^2+2xy+y^2=144
x^2+y^2=144-2xy=126
(x-y)^2=x^2-2xy+y^2=108
x-y=±6√3
(x^1/2-y^1/2)/(x^1/2+y^1/2)
上下乘x^1/2-y^1/2
=(x^1/2-y^1/2)^2/(x^1/2-y^1/2)(x^1/2+y^1/2)
=[x-2(xy)^(1/2)+y]/(x-y)
=(12-2×3)/(±6√3)
=6/(±6√3)
=√3/3或-√3/3
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