TARGET

$\sqrt[5]{\frac{a^{5}+b^{5}}{2}}\doteq \sqrt[5]{\frac{a^{5}+b^{5}}{a^{4}+b^{4}}\frac{a^{4}+b^{4}}{a^{3}+b^{3}}\frac{a^{3}+b^{3}}{a^{2}+b^{2}}\frac{a^{2}+b^{2}}{a+b}\frac{a+b}{2}}$

$\sum \sqrt{a^{2}+5ab+b^{2}}\geq \sum \left ( a+b+\frac{\left ( 2\sqrt{7}-4 \right )ab}{a+b} \right )$