Question

If $x^2+\frac{1}{x^2}=7$, find the values of $x+\frac{1}{x}$.

• A. $\pm 3$
• B. $\pm 4$
• C. $\pm 7$
• D. $\pm 2$

Answer 1

The correct option is A $\pm 3$

$x^2+\frac{1}{x^2}=7$
Now,
$(x+\frac{1}{x}{)}^2=x^2+\frac{1}{x^2}+2(x\left)\right(\frac{1}{x})$
$=7+2$
$=>(x+\frac{1}{x})=\sqrt{9}$
$=>(x+\frac{1}{x})=\pm 3$