分数指数幂的化简求值
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。
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。
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