MathDB

1

Part of 2017 Azerbaijan JBMO TST

Problems(2)

Inequality

Source: Azerbaijan JBMO TST D1,P1.

5/31/2017
Let x,y,z,tx,y,z,t be positive numbers.Prove that xyzt(x+y)(z+t)≤(x+z)2(y+t)24(x+y+z+t)2.\frac{xyzt}{(x+y)(z+t)}\leq\frac{(x+z)^2(y+t)^2}{4(x+y+z+t)^2}.
inequalitiesAzerbaijan
Problem 2

Source: Second Romanian JBMO TST 2016

6/15/2016
a,b,c>0 and abc≥1abc\ge 1.Prove that: 1a3+2b3+6+1b3+2c3+6+1c3+2a3+6≤13\dfrac{1}{a^3+2b^3+6}+\dfrac{1}{b^3+2c^3+6}+\dfrac{1}{c^3+2a^3+6} \le \dfrac{1}{3}
algebraInequality