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Sides of Triangle

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,812
Let $a,\,b,\,c$ be the sides of a triangle. Prove that

$\dfrac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\dfrac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\dfrac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}}\le 3$.