Question

Twice the sum of a number and its reciprocal is $4$. Find the number.

Answer 1

Let the number be $x$.

According to the question,

$2(x+\frac{1}{x})=4$

$x+\frac{1}{x}=\frac{4}{2}$

$\frac{x^2+1}{x}=2$

$x^2+1=2x$

$x^2+1-2x=0$

${(x-1)}^2=0$

$x-1=0$

$x=1$

Hence, the number is $1$.