Question

If $a^2+\frac{1}{a^2}$ = 38, then the value of $a-\frac{1}{a}$ is equal to.

• A. $\pm 4$
• B. $\pm 5$
• C. $\pm 6$
• D. $\pm 7$

Answer 1

The correct option is C $\pm 6$

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

$(a-\frac{1}{a}{)}^2$ = $a^2+\frac{1}{a^2}$ - 2
$\Rightarrow$$(a-\frac{1}{a}{)}^2$ = 38 - 2
$\Rightarrow$$(a-\frac{1}{a}{)}^2$ = 36
$\Rightarrow$$(a-\frac{1}{a})$ = $\pm 6$