Determine the greatest value of the following expression

In summary, the conversation is discussing a problem involving an equation with three positive real roots and determining the greatest value of an expression. The person asking also wants to know what course the problem is from and what progress has been made so far. However, the expert summarizer does not address these questions and only provides a summary of the conversation.
  • #1
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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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  • #2
From what course is this problem taken?

What progress have you made so far?
 
  • #3
simple, i love inequality!(h)
 
  • #4
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.

Your response addresses neither question.
 
  • #5
Thank
But I don't have imagine with my problem
 
  • #6
Was this problem assigned to you by a teacher/professor in a class?

If so, what is the name of the class?
 

FAQ: Determine the greatest value of the following expression

What is the purpose of determining the greatest value of an expression?

The purpose of determining the greatest value of an expression is to find the maximum possible result that can be obtained by substituting different values for the variables in the expression. This can help in solving problems related to optimization, finding the best solution, or identifying the maximum potential of a system or process.

What are the steps involved in determining the greatest value of an expression?

The steps involved in determining the greatest value of an expression may vary depending on the complexity of the expression. However, in general, the steps involve simplifying the expression, identifying the critical points (where the value of the expression changes), and evaluating the expression at those points to determine the greatest value.

Can the greatest value of an expression be negative?

Yes, the greatest value of an expression can be negative. This can happen when the expression involves negative numbers or when the critical points are negative. It is important to consider both positive and negative values when determining the greatest value of an expression.

How do you know when you have found the greatest value of an expression?

You can know when you have found the greatest value of an expression by evaluating the expression at all critical points and comparing the results. The highest value among all the critical points will be the greatest value of the expression. It is also important to check if there are any other restrictions or limitations in the given problem that may affect the greatest value.

Can technology be used to determine the greatest value of an expression?

Yes, technology can be used to determine the greatest value of an expression. With the help of graphing calculators or computer software, the expression can be graphed and the greatest value can be identified by looking at the highest point on the graph. However, it is still important to follow the steps of simplifying the expression and identifying critical points to ensure accuracy.

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