MathDB

(a+b)/c^2+(c+a)/b^2+(b+c)/a^2 >= 9/(a+b+c) +1/a + 1/b + 1/c

Source: Rioplatense Olympiad 2002 level 3 P4

September 6, 2018

algebraInequality3-variable inequalityinequalities

Problem Statement

Let

a, b

and

c

be positive real numbers. Show that

\frac{a+b}{c^2}+ \frac{c+a}{b^2}+ \frac{b+c}{a^2}\ge \frac{9}{a+b+c}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}