Question 762701
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{a\,+\,b}\ +\ \frac{2}{a\,-\,b}\ =\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{a\,+\,b}\ +\ \frac{4}{a\,-\,b}\ =\ \frac{5}{2}] 


This one was very interesting.  Going at it straight up gets you into trouble.  But I noted that the denominators in each of the two equations were the same, so I tried:


Let *[tex \LARGE x\ =\ \frac{1}{a\,+\,b}] and let *[tex \LARGE y\ =\ \frac{1}{a\,-\,b}].  Making the substitutions, the two equations become:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ +\ 2y\ =\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 4y\ =\ \frac{5}{2}]


Solve by elimination to get


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{1}{4}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1}{2}]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ =\ 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ b\ =\ 2]


Solve the simple 2X2 by elimination. 


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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