Question 1117380
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \(\sqrt{3\ +\ \sqrt{5}}\ -\ \sqrt{3\ -\ \sqrt{5}}\)^2\ =^? \ 2]


Expand the binomial in the LHS


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \(3\ +\ \sqrt{5}\)\ -\ 2\(\sqrt{3\ +\ \sqrt{5}}\)\(\sqrt{3\ -\ \sqrt{5}}\)\ +\ \(3\ -\ \sqrt{5}\)\ =^?\ 2]


Collect like terms and calculate the product of conjugates in the center term of the LHS


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  6\ -\ 2\(\sqrt{9\ -\ 5}\)\ =^?\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  6\ -\ 2\(\sqrt{4}\)\ \equiv\ 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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