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Part of 2018 Azerbaijan IZhO TST

Problems(1)

TST Tajikistan 2018 Day 1 Problem 3

Source:

Problem 3. Suppose that the equation x^3-ax^2+bx-a=0 has three positive real roots (b>0). Find the minimum value of the expression: (b-a)(b^3+3a^3)

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