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6 < \sqrt{2x+3}+ \sqrt{2y+3}+ \sqrt{2z+3}<= 3\sqrt5 if x+y+z=3 & x,y,z>0

Source: Mexican Mathematical Olympiad 1992 OMM P5

July 29, 2018
inequalitiesInequalityalgebra

Problem Statement

x,y,zx, y, z are positive reals with sum 33. Show that 6<2x+3+2y+3+2z+3≤356 < \sqrt{2x+3} + \sqrt{2y+3} + \sqrt{2z+3}\le 3\sqrt5
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