MathDB
(x+2/y)(y/x+2)>= 8 if, xy>0

Source: Greece JBMO TST 2013 p1

April 29, 2019
algebrainequalities

Problem Statement

If x,y<0 prove that (x+2y)(yx+2)8\left(x+\frac{2}{y} \right) \left(\frac{y}{x}+2 \right)\geq 8. When do we have equality?