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4/5(1/a+1/b)+2/c>=27/(2(a+b+c)) if a>=8b/5>0 and a>=c>0 over R

Source: Mongolia 1999 Grade 8 P2

May 4, 2021
Inequalityinequalities

Problem Statement

Let a,b,ca,b,c be the real numbers with a≥85b>0a\ge\frac85b>0 and a≥c>0a\ge c>0. Prove the inequality 45(1a+1b)+2c≥272⋅1a+b+c.\frac45\left(\frac1a+\frac1b\right)+\frac2c\ge\frac{27}2\cdot\frac1{a+b+c}.
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