Question by Nguyễn Huy Thắng - Discuss with MathYouLike

Nguyễn Huy Thắng

09/03/2017 at 20:58

Let \(a,b,c\) are positive real number satisfy \(a+b+c=1\). Prove that \(\dfrac{1}{\sqrt{\left (a^2+ab+b^2\right )\left (b^2+bc+c^2\right )}}+\dfrac{1}{\sqrt{\left (b^2+bc+c^2\right )\left (c^2+ca+a^2\right )}}+\dfrac{1}{\sqrt{\left (c^2+ca+a^2\right )\left (a^2+ab+b^2\right )}}\ge 4+\dfrac{8}{\sqrt{3}}\)

inequality

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Nguyen Huu Ai Linh 10/12/2017 at 07:08

That too long!

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