find the cases of equality
Source: Ireland 2001
July 5, 2009
inequalities proposedinequalities
Problem Statement
Prove that for all real numbers with we have:
\sqrt[3]{\frac{a^2 b^2 (a\plus{}b)^2}{4}} \le \frac{a^2\plus{}10ab\plus{}b^2}{12}
and find the cases of equality. Hence, or otherwise, prove that for all real numbers
\sqrt[3]{\frac{a^2 b^2 (a\plus{}b)^2}{4}} \le \frac{a^2\plus{}ab\plus{}b^2}{3}
and find the cases of equality.