if $\sum_{k=1}^nx_{k}=\sum_{k=1}^{n}x_{k}^2=n$ then forall k, $x_k=1$

Question

Let $(x_{k})_{1\leq k\leq n}$ be a set of real numbers such as $\sum_{k=1}^nx_{k}=\sum_{k=1}^{n}x_{k}^2=n$

I need to give proof that $\forall k\in${$1, 2, ..., n$} $x_k=1$

I spent hours trying to solve it but I failed, I'd like a hint about how I should approach it.

Thanks a lot.

Answer 1

What is $\sum_{k=1}^n(x_k-1)^2$?