A) \[\frac{2}{3}\]or \[\frac{3}{2}\]
B) \[\frac{3}{4}\]or \[\frac{4}{3}\]
C) \[\frac{2}{5}\]or \[\frac{5}{2}\]
D) None of these
Correct Answer: A
Solution :
Let the number be x. Then, \[x+\frac{1}{x}=\frac{13}{6}\Rightarrow \frac{{{x}^{2}}+1}{x}=\frac{13}{6}\Rightarrow 6{{x}^{2}}-13x+6=0\]\[\Rightarrow \]\[6{{x}^{2}}-9x-4x+6=0\]\[\Rightarrow \]\[(3x-2)\,(2x-3)=0\] \[\Rightarrow \] \[x=\frac{2}{3}\] or \[x=\frac{3}{2}\]. x 6 x 6 Hence, the required number is \[\frac{2}{3}\] or \[\frac{3}{2}\].
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