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(a^2 + c^2)(a^2 + d^2)(b^2 + c^2)(b^2 + d^2) <= 25 when a+b=c+d=2, a,b,c,d >=0

Source: Singapore Senior Math Olympiad 2012 2nd Round p5 SMO

March 25, 2020
inequalitiesalgebra

Problem Statement

For a,b,c,d≥0a,b,c,d \geq 0 with a+b=c+d=2a + b = c + d = 2, prove (a2+c2)(a2+d2)(b2+c2)(b2+d2)≤25(a^2 + c^2)(a^2 + d^2)(b^2 + c^2)(b^2 + d^2) \leq 25
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