A Geometric Inequality

For discussing Olympiad Level Algebra (and Inequality) problems
Mehedi Hasan Nowshad
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A Geometric Inequality

Unread post by Mehedi Hasan Nowshad » Sat Nov 05, 2016 11:48 am

Let $a,b,c$ be the sides of $\triangle ABC$ and $x$ be any non-negative real number. Prove that,
\[ a^x \cos A+ b^x \cos B + c^x \cos C
\leq \dfrac{1}{2}(a^x+b^x+c^x) . \]
"Failure is simply the opportunity to begin again, this time more intelligently."
- Henry Ford

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Phlembac Adib Hasan
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Re: A Geometric Inequality

Unread post by Phlembac Adib Hasan » Mon Nov 07, 2016 11:32 am

Hint:
Chebyshev’s Inequality
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