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a,b,c,d,e>0 min d , (x + a)(x + b)(x + c)=x^3+3dx^2+3x+e^3 (HOMC 2013 J Q11)

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July 28, 2019
algebrapolynomialminimum

Problem Statement

The positive numbers a,b,c,d,ea, b, c,d,e are such that the following identity hold for all real number xx: (x+a)(x+b)(x+c)=x3+3dx2+3x+e3(x + a)(x + b)(x + c) = x^3 + 3dx^2 + 3x + e^3. Find the smallest value of dd.
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