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IMO 2006 — Complete Shortlist Question 5

IMO Shortlist · IMO 2006 — Complete Shortlist

Question 5

Let $a, b, c$ be the sides of a triangle. Prove that
$$
\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\frac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}} \leq 3 .
$$