Cauchy-Schwarz: Problema 1

Let \(x_1, x_2, \ldots, x_{n+1} > 0\) such that \(x_1+x_2+
\ldots x_n = x_{n+1}\). Prove that: $$\sum_{i=1}^{n} \sqrt{
x_{i}(x_{n+1}-x_{i})} \leq \sqrt{ \sum_{i=1}^{n} x_{n+1}(x_{n+1} –
x_{i})}.$$