Discussion
The sum of a rational number and its reciprocal is 13/6, find the number
Answer: A
The number is 2/3 or 3/2.
Let the number be \(x\). Then:
\[ \begin{aligned} x + \tfrac{1}{x} &= \tfrac{13}{6} \\ 6x^{2} - 13x + 6 &= 0 \\ (2x - 3)(3x - 2) &= 0 \end{aligned} \]
so \(x = 3/2\) or \(2/3\). Check: \(2/3 + 3/2 = 4/6 + 9/6 = 13/6\). 3/4 + 4/3 = 25/12 and 2/5 + 5/2 = 29/10, so those pairs fail.
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