Discussion
Sum of a rational number and its reciprocal is \(\dfrac {13}{6}\). Find the number.
Answer: B
Let,
\(x + \dfrac{1}{x} = \dfrac{13}{6}\\
\Rightarrow \dfrac{x^2+1}{x} = \dfrac{13}{6}\\
\Rightarrow 6x^2-13x+6 = 0\\
\Rightarrow 6x^2-9x-4x+6 = 0\\
\Rightarrow (3x-2)(2x-3)\\
\Rightarrow x = \dfrac{2}{3} \text{ or } \dfrac{3}{2}\)
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