MathDB
Inequality

Source: Greek national M.O. 2003, Final Round,problem 1

November 15, 2011
inequalitiesfunctioncalculusderivativeinequalities unsolved

Problem Statement

If a,b,c,da, b, c, d are positive numbers satisfying a3+b3+3ab=c+d=1,a^3 + b^3 +3ab = c + d = 1, prove that (a+1a)3+(b+1b)3+(c+1c)3+(d+1d)3≥40.\left(a+\frac{1}{a}\right)^3+\left(b+\frac{1}{b}\right)^3+\left(c+\frac{1}{c}\right)^3+\left(d+\frac{1}{d}\right)^3\geq 40.
Back to ProblemsView on AoPS