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MathNet 2011 Question 2

Math Olympiad Vault · MathNet 2011

Question 2

Prove that if positive numbers $a$, $b$, $c$, $k$, $l$, $m$ satisfy the inequalities $abc \ge ka + lb + mc$, then they satisfy the inequality
$$
a + b + c \ge \sqrt{3}(\sqrt{k} + \sqrt{l} + \sqrt{m}).
$$