Solving for x with a Square Root Sign: Help Needed!

In summary, the conversation is about solving for x in the equation x + \sqrt{x} = 6. The participants discuss different methods, such as isolating the square root, substituting u = sqrt(x), and factorizing. They also caution about spurious roots when squaring both sides of the equation.
  • #1
Jules18
102
0
Does anyone know how to solve for x in the following equation:

x + [tex]\sqrt{x}[/tex] = 6

I don't know how to solve for x with eq'ns like this, and I'm studying inverse fxns right now, so I'm told that's what I'm supposed to do.

The square root sign is throwing me off.
The first time I tried, I tried squaring both sides to get rid of the sq. root sign, but it just made it more complicated.
Any suggestions?

~Jules~
 
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  • #2
you need to isolate the sqrt(x), it will make everything A LOT nicer looking
 
  • #3
Try substituting u = sqrt(x).
 
  • #4
It is a quadradic in sqrt(x)
factorize into the form
x+sqrt(x)-6=(a*sqrt(x)+b)(c*sqrt(x)+d)
 
  • #5
Three basically different methods, all of which work! I would prefer emyt's method:
write the equation as [itex]\sqrt{x}= 6- x[/itex] and square both sides. Caution: squaring both sides of an equation (or, more generally, multiplying both sides of an equation by something involving the unknown) can introduce "spurious roots" so be sure to check any solution in the original equation.
 

1. How do I solve for x with a square root sign?

To solve for x with a square root sign, you need to isolate the square root term on one side of the equation and then square both sides to eliminate the square root. This will give you a regular algebraic equation that can be solved using standard algebraic techniques.

2. What is the first step in solving for x with a square root sign?

The first step is to identify the square root term in the equation and isolate it on one side of the equation by moving all other terms to the other side. This will make it easier to eliminate the square root in the next step.

3. Can I just square both sides of the equation to solve for x with a square root sign?

No, you cannot just square both sides of the equation. You must first isolate the square root term on one side and then square both sides to eliminate the square root. Squaring both sides without isolating the square root term can lead to incorrect solutions.

4. Is there a shortcut for solving for x with a square root sign?

There is no shortcut for solving for x with a square root sign. You must follow the steps of isolating the square root term and then squaring both sides to eliminate the square root. However, you can use a calculator to simplify the square root if needed.

5. Can I solve for x with a square root sign if there are other terms in the equation?

Yes, you can still solve for x with a square root sign even if there are other terms in the equation. The key is to isolate the square root term on one side and then square both sides to eliminate the square root. You can then solve the resulting algebraic equation using standard algebraic techniques.

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