Very strange inequality..

For discussing Olympiad Level Algebra (and Inequality) problems
Katy729
Posts: 47
Joined: Sat May 06, 2017 2:30 am

Very strange inequality..

Unread post by Katy729 » Sun Jun 18, 2017 10:43 pm

Let $a$,$b$,$c$ be real positive numbers. Prove that
\[\left(\frac{a^3+abc}{b+c}\right)+\left(\frac{b^3+abc}{c+a}\right)+\left(\frac{c^3+abc}{a+b}\right)\ge a^2+b^2+c^2\]
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Katy729
Posts: 47
Joined: Sat May 06, 2017 2:30 am

Re: Very strange inequality..

Unread post by Katy729 » Sat Jul 01, 2017 3:24 pm

Let $a$,$b$,$c$ be real positive numbers. Prove that
\[\left(\frac{a^3+abc}{b+c}\right)+\left(\frac{b^3+abc}{c+a}\right)+\left(\frac{c^3+abc}{a+b}\right)\ge a^2+b^2+c^2\]

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