Question

If $x-\frac{1}{x}=\sqrt{5},$ then the value of $x+\frac{1}{x}$ is
$(x>0)$

• A. $7$
• B. $\sqrt{7}$
• C. $5$
• D. $3$

Answer 1

The correct option is D $3$

$x-\frac{1}{x}=\sqrt{5}$
$\Rightarrow {(x-\frac{1}{x})}^2=5=x^2+\frac{1}{x^2}-2\times x\times \frac{1}{x}$
$\Rightarrow x^2+\frac{1}{x^2}=7$
$\Rightarrow x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}=7+2$
$\Rightarrow {(x+\frac{1}{x})}^2=9$
$\Rightarrow (x+\frac{1}{x})=3$