Problem

Source: Moldova National MO 2008, 12 Grade, Problem 1

Tags: algebra proposed, algebra, polynomial, calculus, inequalities



Consider the equation $ x^4 - 4x^3 + 4x^2 + ax + b = 0$, where $ a,b\in\mathbb{R}$. Determine the largest value $ a + b$ can take, so that the given equation has two distinct positive roots $ x_1,x_2$ so that $ x_1 + x_2 = 2x_1x_2$.