分数指数幂的化简求值
问题描述：
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
答
x+y=12两边平方x^2+2xy+y^2=144x^2+y^2=144-2xy=126(x-y)^2=x^2-2xy+y^2=108x-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...