Discussion
The sum of a positive number and its reciprocal is \(\dfrac{10}{3}\). The greater of the possible values is:
Answer: C
From \(x + \dfrac{1}{x} = \dfrac{10}{3}\), multiplying through by \(3x\) gives \(3x^2 - 10x + 3 = 0\). Factoring, \((3x - 1)(x - 3) = 0\), so \(x = 3\) or \(x = \dfrac{1}{3}\). The two roots are always reciprocals of each other, and the greater is 3.
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