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Source: Old and New Inequalities, problem 105; Vietnam MO 2004 Group A, created by Namdung

August 17, 2005
inequalitiesalgebrapolynomialfunctionlimitquadraticsreal analysis

Problem Statement

Let xx, yy, zz be positive reals satisfying (x+y+z)3=32xyz\left(x+y+z\right)^{3}=32xyz Find the minimum and the maximum of P=x4+y4+z4(x+y+z)4P=\frac{x^{4}+y^{4}+z^{4}}{\left(x+y+z\right)^{4}}
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