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# How to solve this equation?

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Hi everybody,

in my micro-economics class my tutor solved a problem for us. There was a particular step which I didn't quite understand. How did he manage to transform this equation:

into this one:

What are the computation steps inside the square root which he performed in order to bring "L - the fration^2 * x^2" to the same denominator?

Thank you very much in advance!

Guest Jun 26, 2014

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Alan  Jun 26, 2014
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Have you written them down correctly?  These two functions are clearly not equivalent.  For example:

Alan  Jun 26, 2014
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$$L-K\neq\left( \sqrt{L}+\sqrt{K} \right)^2$$

heureka  Jun 26, 2014
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You are right. I'm sorry, I made a mistake... the first equation should be (a "+" not a "-" there):

Then that means, that he only brought the "L - (the big fraction)^2 * X^2" to the same denominator resulting in:

and then he simplified the "L^2" and the "(Sqrt(L)+Sqrt(K))^2" inside of the big sqare root with the fraction outside of the square root thus resulting in:

Does this make sense to you?

Thank you!

Guest Jun 26, 2014
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$$\dfrac{L}{\sqrt{L}}*\sqrt{(\sqrt{L}+\sqrt{K})^2-x^2}$$

heureka  Jun 26, 2014
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