Question

If $a^2+\frac{1}{a^2}=10$, then the value of $a^4+\frac{1}{a^4}$ is

• A. $90$
• B. $98$
• C. $100$
• D. $102$

Answer 1

Answer: (B)

$98$

Given, $a^2+\frac{1}{a^2}=10$.

On squaring both sides, we get,

$\Rightarrow {(a^2+\frac{1}{a^2})}^2={\left(10\right)}^2$.

We know, $(a+b{)}^2=a^2+2ab+b^2$.

Then,
$\Rightarrow (a^2{)}^2+(\frac{1}{a^2}{)}^2+2\left(a^2\right)\left(\frac{1}{a^2}\right)=100$

$\Rightarrow a^4+\frac{1}{a^4}+2=100$

$\Rightarrow a^4+\frac{1}{a^4}=100-2$

$\Rightarrow a^4+\frac{1}{a^4}=98$.

Therefore, option $B$ is correct.