Question

If $a^2+\frac{1}{a^2}=23$, then find $a+\frac{1}{a}$.

• A. 20
• B. 25
• C. 5
• D. 4

Answer 1

The correct option is C 5

Applying the formula, ${(a+b)}^2=a^2+b^2+2ab$
${(a+\frac{1}{a})}^2=a^2+{\left(\frac{1}{a}\right)}^2+2a\times \frac{1}{a}=a^2+\frac{1}{a^2}+2$

So, ${(a+\frac{1}{a})}^2=a^2+\frac{1}{a^2}+2$

Substituting $a^2+{\left(\frac{1}{a}\right)}^2=23$,
$=>{(a+\frac{1}{a})}^2=23+2=25$

$a+\frac{1}{a}=\sqrt{25}=5$