Question 190063
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A number: <i>x</i>


The reciprocal of the number:  *[tex \LARGE \frac{1}{x} ]


So,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x + \frac{1}{x} = \frac{25}{12} ] 


LCD on the left is <i>x</i>, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2 + 1}{x} = \frac{25}{12} ] 


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12(x^2 + 1) = 25x]


Distribute, collect like terms, put in standard form and solve the quadratic.  Check both roots because you may have to exclude one of them since squaring the variable in the process of solving the problem can introduce extraneous roots. (Although, in this particular case, both roots should prove valid)


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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