Question 35
Prove that if $a, b, c \geq 1$ and $a+b+c=9$, then
$$
\sqrt{a b+b c+c a} \leq \sqrt{a}+\sqrt{b}+\sqrt{c}
$$
$$
\sqrt{a b+b c+c a} \leq \sqrt{a}+\sqrt{b}+\sqrt{c}
$$
MathNet 2004 — Part 01 Question 35
Math Olympiad Vault · MathNet 2004 — Part 01