文 [1]、[2 ]就方程 ax =x根的分布情况作了讨论 ,但很繁琐又不清晰 ,实际上 ,只要讨论函数 y =x1 x 的性质 ,方程 ax =x根的分布就显得十分清楚了 ,为此 ,特介绍如下方法 .定理　函数 f(x) =x1 x(x 0 ) ,(1)在 x =e处 ,f (x)取最大值 e1 e;(2 ) 0 x e时 ,f (x)递增 ;x e时 The paper [1], [2] discusses the distribution of the equation ax =x, but it is tedious and unclear. In fact, as long as the function y =x1 x is discussed, the distribution of the equation ax =x becomes It is very clear, for this purpose, we introduce the following method. Theorem function f(x) = x1 x(x 0), (1) At x = e, f (x) takes the maximum value e1 e; (2) 0 xe When, f (x) is incremented; when xe