Question

If $a^2+\frac{1}{a^2}$ = 23, then the value of $a+\frac{1}{a}$ is equal to .

• A. $\pm 2$
• B. $\pm 3$
• C. $\pm 5$
• D. $\pm 7$

Answer 1

The correct option is C $\pm 5$

Using the identity,
$(a+b{)}^2=a^2+b^2+2ab$,

$(a+\frac{1}{a}{)}^2$ = $a^2+\frac{1}{a^2}$ + 2
$\Rightarrow$$(a+\frac{1}{a}{)}^2$ = 23 + 2
$\Rightarrow$$(a+\frac{1}{a}{)}^2$ = 25
$\Rightarrow$$(a+\frac{1}{a})$ = $\pm 5$