Suppose $x_0$ , $x_1$ , $x_2$ , ... , $x_n$ are distinct real numbers , prove that :
$ \large{\displaystyle{\sum_{i=0}^{n} \left( x_{i}^{n}\prod_{\substack{0\leq k\leq n \\ k\neq i }}\frac{x-x_k}{x_i-x_k} \right)=x^n}} $
I have no ideas to do this question