Question

If $a+\frac{1}{a}=3$, then the value of $a^2+\frac{1}{a^2}$ is:_____.

• A. 27
• B. 7
• C. 9
• D. 3

Answer 1

The correct option is B 7

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

$(a+\frac{1}{a}{)}^2=a^2+2\times a\times \frac{1}{a}+\frac{1}{a^2}$
$\Rightarrow$ $3^2=(a^2+\frac{1}{a^2})+2$
$\Rightarrow$ $(a^2+\frac{1}{a^2})=7$.