Question

If $a+\frac{1}{a}=2$, find $\frac{a^4+1}{a^2}$.

• A. $7$
• B. $8$
• C. $6$
• D. $2$

Answer 1

The correct option is D $2$

Given,
$\frac{a^4+1}{a^2}$
$=\frac{a^4}{a^2}+\frac{1}{a^2}$
$=a^2+\frac{1}{a^2}$
Now,
$a+\frac{1}{a}=2$
Squaring both sides,
$=>(a+\frac{1}{a}{)}^2=2^2$
$=>a^2+\frac{1}{a^2}+2\left(a\right)\left(\frac{1}{a}\right)=4$
$=>a^2+\frac{1}{a^2}=4-2$
$=>a^2+\frac{1}{a^2}=2$