Question

If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

• A. 4
• B. 3
• C. 1
• D. 2

Answer 1

The correct option is D

2

Suppose the number be $x.$
According to the given condition
$x-\frac{2}{x}=1$
$x^2-2=x$
$x^2-x-2=0$

Using quadratic formula,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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

$\Rightarrow x=\frac{1\pm \sqrt{1+8}}{2}\Rightarrow x=\frac{1\pm 3}{2}$
$\Rightarrow x=2or-1$

As the number is positive, ignore negative value.
Hence, $x=2.$
​$\therefore$ The required number is 2.