Question

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

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (C)

2

Applying the formula, ${(a+b)}^2=a^2+b^2+2ab$
${(a+\frac{1}{a})}^2=a^2+{\left(\frac{1}{a}\right)}^2+2a\times \frac{1}{a}=a^2+\frac{1}{a^2}+2$
$=>a^2+\frac{1}{a^2}={(a+\frac{1}{a})}^2-2$
Substituting $a+\frac{1}{a}=2$,
$=>a^2+\frac{1}{a^2}=2^2-2=4-2=2$