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\sqrt{7x+3}+ \sqrt{7y+3}+\sqrt{7z+3} \le 7 when x,y,z have sum 1

Source: Switzerland - Swiss TST 2000 p6

February 19, 2020
inequalitiesSumalgebra

Problem Statement

Positive real numbers x,y,zx,y,z have the sum 11. Prove that 7x+3+7y+3+7z+3≤7\sqrt{7x+3}+ \sqrt{7y+3}+\sqrt{7z+3} \le 7. Can number 77 on the right hand side be replaced with a smaller constant?
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