Let {c1, x2,..., xn} C R be a subset of real numbers. Prove that \left(x_{1}+x_{2}+\cdots+x_{n}\right)^{2} \leq n\left(x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}\right) Hint: take square roots, write the LHS as a dot product of two

vectors, and use the Cauchy-Schwarz inequality.