Question

If $(x^2+\frac{1}{x^2}=7)$ , find $x-\frac{1}{x}$

• A. $\pm$$\sqrt{(}5)$
• B. 5
• C. -5
• D. $\pm$$\sqrt{(}7)$

Answer 1

The correct option is A

$\pm$$\sqrt{(}5)$

Given
$(x^2+\frac{1}{x^2}=7)$
$x-\frac{1}{x}$
Squaring we get
$(x-\frac{1}{x}{)}^2$ = $x^2+\frac{1}{x^2}-2$ (Using $(a+b{)}^2$)
= ($7-2)$
= 5
Taking Square root on both sides , we get
$(x-\frac{1}{x})$ = $\pm$$\sqrt{(}5)$