MathDB

Prove this 5 variable inequality

Source: 2019 Jozsef Wildt International Math Competition

May 20, 2020

inequalities

Problem Statement

Let

a

b

c

d

e

be real strictly positive real numbers such that

abcde = 1

. Then is true the following inequality:

\frac{de}{a(b+1)}+\frac{ea}{b(c+1)}+\frac{ab}{c(d+1)}+\frac{bc}{d(e+1)}+\frac{cd}{e(a+1)}\geq \frac{5}{2}