A Geometric Inequality
Posted: 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,
\[ a^x \cos A+ b^x \cos B + c^x \cos C
\leq \dfrac{1}{2}(a^x+b^x+c^x) . \]
\[ a^x \cos A+ b^x \cos B + c^x \cos C
\leq \dfrac{1}{2}(a^x+b^x+c^x) . \]