Prove that: $\sqrt{x^2+21}+\sqrt{2y^2+14}+\sqrt{z^2+91}\ge 19$

Prove that: $\sqrt{x^2+21}+\sqrt{2y^2+14}+\sqrt{z^2+91}\ge 19$

Let $x, y, z$ be real number such that $xy+yz+zx=11$. Prove the inequality:
$$\sqrt{x^2+21}+\sqrt{2y^2+14}+\sqrt{z^2+91}\ge 19$$
I think that inequality can be solved by Minkowski....But I couldn't
continue...