Cool inequality

Algebra Level 4

What is the smallest real number n n , such that for any triangle of sides a , b , c a, b, c ,

b + c a b + c a + c + a b c + a b + a + b c a + b c n \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{n}


The answer is 3.

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2 solutions

Mohammed Imran
Apr 2, 2020

The answer is true directly from Ravi Substitution

a=b=c (:

Ravi's substitution??

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