Question 78
Let $a$, $b$, $c$ be real numbers such that $a+b+c+ab+bc+ca+abc \geq 7$. Prove that
$$
\sqrt{a^{2}+b^{2}+2}+\sqrt{b^{2}+c^{2}+2}+\sqrt{c^{2}+a^{2}+2} \geq 6
$$
$$
\sqrt{a^{2}+b^{2}+2}+\sqrt{b^{2}+c^{2}+2}+\sqrt{c^{2}+a^{2}+2} \geq 6
$$
MathNet 2018-part-05 — 181 problems (EN–VI) Question 78
Math Olympiad Vault · MathNet 2018-part-05 — 181 problems (EN–VI)