对任意实数x∈R,定义函数y=[x]为不超过x的最大整数,函数y=[x]称为高斯函数.一、解高斯方程求解含[x]的方程,通常采用变量代换、整除性的讨论、利用[x]的性质等方法把方程转换成不等式,通过讨论不等式的解求解出原方程的解.例1(2013年福建省数学竞赛)求方程sinπx=[2/x-[2/x]+1/2]在区间[0,2π]内的所有实数根 For any real number x∈R, the function y = [x] is defined as the largest integer not exceeding x, and the function y = [x] is called the Gaussian function. First, solve the Gaussian equation to solve the equation with [x] For example, in the discussion of inequality, the solution of the original equation can be obtained by discussing the properties of [x], etc. Example 1 (Fujian Provincial Mathematics Contest 2013) Find the equation sinπx = [2 / x- [2 / x] +1/2] All real roots within the interval [0,2π]