Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:
Option 1: $5 \sqrt{5}$
Option 2: $4 \sqrt{5}$
Option 3: $2 \sqrt{5}$
Option 4: $3 \sqrt{5}$
Correct Answer: $2 \sqrt{5}$
Solution :
Given:
$a-\frac{1}{a}=4$
Squaring both sides, we get,
⇒ $a^2+\frac{1}{a^2}-2=16$
⇒ $a^2+\frac{1}{a^2}=16+2$
⇒ $a^2+\frac{1}{a^2}=18$
Adding 2 on both sides, we get,
⇒ $a^2+\frac{1}{a^2}+2=18+2$
⇒ $(a+\frac{1}{a})^2=20$
$\therefore a+\frac{1}{a}=2\sqrt5$
Hence, the correct answer is $2\sqrt5$.
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