Question

The sum of a number and its reciprocal is $\frac{125}{22}$. The number is

• A. $\frac{2}{11}$
• B. $\frac{1}{11}$
• C. $\frac{3}{11}$
• D. None of these

Answer 1

Answer: (A)

$\frac{2}{11}$

Let the number be $x$,
Thus,

$x+\frac{1}{x}=\frac{125}{22}$
$\Rightarrow 22(x^2+1)=125x$
$\Rightarrow 22x^2-125x+22=0$
$\Rightarrow x=\frac{125\pm \sqrt{{125}^2-4\times 22\times 22}}{2\times 22}$
$\Rightarrow x=\frac{11}{2}or\frac{2}{11}$