Question 1039700
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First you say symbolically:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(t^{\frac{1}{2}}\ -\ 2^{\frac{3}{2}}\right)\left(t^{\frac{1}{2}}\ +\ 2^{\frac{3}{2}}\right)]


And then you write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(t\sqrt{\frac{1}{2}}\ -\ 2\sqrt{\frac{3}{2}}\right)\left(t\sqrt{\frac{1}{2}}\ +\ 2\sqrt{\frac{3}{2}}\right)]


Two vastly different things.  Furthermore, you don't actually ask a question, tell us what you want, or tell us what it is that you are having difficulty understanding.  It is really rather unfair of you to make us guess what you want.


But since I have to guess, I'll guess that you meant the first expression and that you want to find the product of the two binomials.


Note that *[tex \Large a^{\frac{m}{n}}\ =\ \sqrt[n]{a^m}] so *[tex \Large 2^{\frac{3}{2}}\ =\ \sqrt{8}] and *[tex \Large t^{\frac{1}{2}}\ =\ \sqrt{t}]


So you actually have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\sqrt{t}\ -\ \sqrt{8}\right)\left(\sqrt{t}\ +\ \sqrt{8}\right)]


which is the product of a pair of binomial conjugates that results in the difference of two squares; recall *[tex \Large (a\ -\ b)(a\ +\ b)\ =\ a^2\ -\ b^2]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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