# Determine the greatest value of the following expression

#### max

##### New member
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:

$$\displaystyle P=\frac{11a^2-3\sqrt3ab-\frac{1}{3}}{9b-10\left ( \sqrt3a-1 \right )}$$

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#### MarkFL

Staff member
From what course is this problem taken?

What progress have you made so far?

#### max

##### New member
simple, i love inequality!(h)

#### MarkFL

Staff member
I asked from what course the problem is taken, so that I could determine if this sub-forum is the best choice.

I asked what you progress so far has been so that our helpers will know just where you are stuck, and be able to provide meaningful help.

#### max

##### New member
Thank
But I don't have imagine with my problem