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min of x^2 + xy + y^2 / + 2^6 /(x + y)+ 3^4 /x^3 for x,y>0

Source: 2014 Saudi Arabia Pre-TST 3.2

September 13, 2020

algebramininequalities

Problem Statement

Let

x, y

be positive real numbers. Find the minimum of

x^2 + xy +\frac{y^2}{2}+\frac{2^6}{x + y}+\frac{3^4}{x^3}