Question

The sum of a number and its reciprocal is one-fifth of 26. The number is.

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

According to question, $x+\frac{1}{x}=\frac{26}{5}$
$\Rightarrow$$\frac{x^2+1}{x}=\frac{26}{5}$
$\Rightarrow$$5(x^2+1)=26x$
$\Rightarrow$$5x^2+5=26x$
$\Rightarrow$$5x^2-26x+5=0$
$\Rightarrow$$5x^2-25x-x+5=0$
$\Rightarrow$$5x(x-5)-1(x-5)=0$
$\Rightarrow$$(5x-1)(x-5)=0$
$\Rightarrow$$x=5,\frac{1}{5}$