1) $(\sqrt{a}+\sqrt{b})^{8}\geq 64ab(a+b)^{2}$
2) $\sqrt[3]{a}+\sqrt[3]{b}\geq 2^{8}ab(a+b)$
3) $(\frac{x}{y}+\frac{y}{x})^{32}\geq 8^{9}(\frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}})^{4}(\frac{x^{4}}{y^{4}}+\frac{y^{4}}{x^{4}})$
4) $(\frac{x}{y}+\frac{y}{x})^{70}\geq 16^{16}(\frac{x^{3}}{y^{3}}+\frac{y^{3}}{x^{3}})^{5}(\frac{x^{5}}{y^{5}}+\frac{y^{5}}{x^{5}})$
Edited by quanrrom97, 04-03-2013 - 11:52.