Question

If $a^2-3a-1=0$ find the value of $a^2+\frac{1}{a^2}$.

• A. $13$
• B. $18$
• C. $11$
• D. $3$

Answer 1

The correct option is C $11$

$a^2-3a-1=0$
$=>a^2-1=3a$
$=>a-\frac{1}{a}=3$
Squaring both sides,
$=>(a-\frac{1}{a}{)}^2=3^2$
$=>a^2+{\frac{1}{a}}^2-2\left(a\right)\left(\frac{1}{a}\right)=9$
$=>a^2+{\frac{1}{a}}^2=9+2$
$=11$