# Thread: Determine the greatest value of the following expression

1. ## Determine the greatest value of the following expression

Given that the equation $ax^3-x^2+ax-b=0$ ( $a\neq 0,b\neq 0$) has three positive real roots. Determine the greatest value of the following expression
$P=\frac{11a^2-3\sqrt3ab-\frac{1}{3}}{9b-10\left ( \sqrt3a-1 \right )}$

2. ## Re: Determine the greatest value of the following expression

Thanks for your nice equation.I have a learn new thinks from here.

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