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Inequality from Iranian TST 2017

Source: Iran TST 2017, Exam 1, Day 1, Problem 1

April 5, 2017
algebrainequalitiesIranIranian TST

Problem Statement

Let a,b,c,da,b,c,d be positive real numbers with a+b+c+d=2a+b+c+d=2. Prove the following inequality: (a+c)2ad+bc+(b+d)2ac+bd+4≥4(a+b+1c+d+1+c+d+1a+b+1).\frac{(a+c)^{2}}{ad+bc}+\frac{(b+d)^{2}}{ac+bd}+4\geq 4\left ( \frac{a+b+1}{c+d+1}+\frac{c+d+1}{a+b+1} \right).
Proposed by Mohammad Jafari
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