Question

The sum of a number and its reciprocal is $\frac{26}{5}$. Find numbers.

• A. $3$,$\frac{1}{3}$
• B. 6, $\frac{1}{6}$
• C. 5, $\frac{1}{5}$
• D. None

Answer 1

Answer: (C)

5, $\frac{1}{5}$

Let the number = $x$
Thenits reciprocal = $\frac{1}{x}$
$x+\frac{1}{x}=\frac{26}{5}$
$\frac{x^2+1}{x}-\frac{26}{5}=0$
$5x^2+5-26x=0$
$5x^2-25x-x+5=0$
$(x-5)(5x-1)=0$
$x=5,x=\frac{1}{5}$