MathDB

5

Part of 2008 Singapore Senior Math Olympiad

Problems(1)

(1+a^2)(1+b^2)(1+c^2)/(1+a)(1+b)(1+c)>= \frac12 (1+abc) for a,b,c>=0

Source: Singapore Senior Math Olympiad 2008 2nd Round p5 SMO

3/25/2020
Let a,b,c≥0a,b,c \ge 0. Prove that (1+a2)(1+b2)(1+c2)(1+a)(1+b)(1+c)≥12(1+abc)\frac{(1+a^2)(1+b^2)(1+c^2)}{(1+a)(1+b)(1+c)}\ge \frac12 (1+abc)
inequalitiesalgebra