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题目:已知正实数x,y满足xy=x+y/x-y,求实数x的最小值.此题的形式很容易想到可以把它变形为x=f(y)的形式,即将x表示为y的函数,进而求其最值.但在变形时发现,并不能直接很容易的表示,这成为此题的难点,但这种方法也是可操作的.方法一:原式变形为x~2y-xy~2=x+y(*),可整理为关于x的方程,即为yx~2-(y~2+1)x-y=0,利用求根公式可得x=
Title: Knowing the positive real number x, y satisfies the minimum value of xy = x + y / xy and finding the real number x The form of this question is easy to think of as a form that can be transformed into x = f (y) Of the function, and then find the best value, but found in the deformation, and can not be directly expressed easily, which became the problem of difficulty, but this method is also operable.Method one: the original deformation of x ~ 2y- xy ~ 2 = x + y (*), can be sorted into the equation about x, which is yx ~ 2- (y ~ 2 +1) xy = 0,