Dec 26, 2020 Thread starter Admin #1 anemone MHB POTW Director Staff member Feb 14, 2012 3,812 Let $a,\,b,\,c$ be the sides of a triangle. Prove that $\dfrac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\dfrac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\dfrac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}}\le 3$.

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