Problem 6 of RMO 2007 (Regional Mathematical Olympiad-India)
Source: Elementry inequality
September 13, 2009
inequalities unsolvedinequalities
Problem Statement
Prove that:
(a) 5<\sqrt {5}\plus{}\sqrt [3]{5}\plus{}\sqrt [4]{5}
(b) 8>\sqrt {8}\plus{}\sqrt [3]{8}\plus{}\sqrt [4]{8}
(c) n>\sqrt {n}\plus{}\sqrt [3]{n}\plus{}\sqrt [4]{n} for all integers
[Weightage 16/100]