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Found problems: 1

2009 Singapore Senior Math Olympiad, 4
Tags: inequalities , logarithms , weighted am gm
Given that $ a,b,c, x_1, x_2, ... , x_5 $ are real positives such that $ a+b+c=1 $ and $ x_1.x_2.x_3.x_4.x_5 = 1 $. Prove that \[ (ax_1^2+bx_1+c)(ax_2^2+bx_2+c)...(ax_5^2+bx_5+c)\ge 1\]