Question

When a particular number is added to its own reciprocal, the resulting sum is $2$. Find the number.

• A. $-2$
• B. $-1$
• C. $-\frac{1}{2}$
• D. $1$
• E. $2$

Answer 1

The correct option is D $1$

Let the number be $x$
As per the problem,
$x+\frac{1}{x}=2$
$\Rightarrow \frac{x^2+1}{x}=2$
$\Rightarrow x^2+1=2x$
$\Rightarrow x^2-2x+1=0$
$\Rightarrow x^2-x-x+1=0$
$\Rightarrow x(x-1)-1(x-1)=0$
$\Rightarrow (x-1)(x-1)=0$
$\Rightarrow x-1=0$
$\Rightarrow x=1$