The sum of a rational number and its reciprocal is 13/6. Find the number. · ABC26GN1629
Subject: General Aptitude · Chapter: Problems on Numbers
The sum of a rational number and its reciprocal is $\frac{13}{6}$. Find the number.
Answer
No answer key was printed for this question.
Explanation
Let the number be $x$. Then, $x+\frac{1}{x}=\frac{13}{6} \Rightarrow \frac{x^{2}+1}{x}=\frac{13}{6} \Rightarrow 6x^{2}-13x+6=0 \Rightarrow 6x^{2}-9x-4x+6=0 \Rightarrow (3x-2)(2x-3)=0 \Rightarrow x=\frac{2}{3} \text{ or } x=\frac{3}{2}$. Hence, the required number is $\frac{2}{3}$ or $\frac{3}{2}$.
Explanation as extracted from the printed page; notation may be imperfect.