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min (a+b)(b+c)/(a+2b+c), 1<=a,b,c<=2 (I Soros Olympiad 1994-95 R1 9.3 10.2)

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July 30, 2021
algebrainequalitiesmin

Problem Statement

Find the smallest possible value of the expression (a+b)(b+c)a+2b+c\frac{(a+b) (b + c)}{a + 2b+c} where a,b,ca, b, c are arbitrary numbers from the interval [1,2][1,2].
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