Question 428153
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I already did this one today.  But here it is again in case you missed it.


Let  *[tex \Large x] represent the number.  Then  *[tex \Large \frac{1}{x}] is the reciprocal of the number, and  *[tex \Large \frac{6}{x}] is 6 times the reciprocal.  The sum is 5, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ \frac{6}{x}\ =\ 5]


Multiply by *[tex \Large x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 6\ =\ 5x]


Put the quadratic into standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 5x\ +\ 6\ =\ 0]


Solve the quadratic for *[tex \Large x].  Hint: it factors.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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