Let $ (u_1, u_2, u_3, u_4)$ and $ (v_1, v_2, v_3, v_4)$ be vectors in $ \mathbb R_+^4$ . Is the following inequality true? \begin{align*} \left(\sum_{{4 \choose 3}} \sqrt{u_i u_j u_k}\right)^{2/3} + \left(\sum_{{4 \choose 3}} \sqrt{v_i v_j v_k}\right)^{2/3} \leq \left(\sum_{{4 \choose 3}} \sqrt{(v_i+u_i) (v_j+u_j) (v_k+u_k)}\right)^{2/3} \end{align*} Here $ \sum_{{4 \choose 3}}$ refers to $ \sum_{1\leqRead more