Question

If twice the reciprocal of a positive number is subtracted from the same number, we get 1. Find the number.

• A. 3
• B. 2
• C. 1
• D. 4

Answer 1

The correct option is B 2

Let the number be $x$.
Reciprocal of a number = $\frac{1}{x}$
Twice the reciprocal = $\frac{2}{x}$

According to the given condition,
$x-\frac{2}{x}=1$
$x^2-2=x$
$x^2-x-2=0$

Quadratic formula is given by,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here, $a=1,b=-1$ and $c=-2$

$\Rightarrow x=\frac{1\pm \sqrt{1-(4\times 1\times -2)}}{2}$

$=\frac{1\pm \sqrt{1+8}}{2}$

$=\frac{1\pm \sqrt{9}}{2}$

$=\frac{1\pm 3}{2}$

$\Rightarrow x=2,-1$

As the number is positive, ignore negative value.

Hence, $x$ = 2
​$\therefore$ The required number is 2.