MCQ
The square root of $a^2+\frac{1}{a^2}+2$ is
- ✓$a+\frac{1}{a}$
- B$a-\frac{1}{a}$
- C$a^2+\frac{1}{a^2}$
- D$a^2-\frac{1}{a^2}$
✓
Answer
Correct option: A.
$a+\frac{1}{a}$
(a)
We find that
$a^2+\frac{1}{a^2}+2=a^2+\frac{1}{a^2}+2 \times a \times \frac{1}{a}=\left(a-\frac{1}{a}\right)^2$
So, the square root of $a^2+\frac{1}{a^2}+2$ is $a+\frac{1}{a}$.
We find that
$a^2+\frac{1}{a^2}+2=a^2+\frac{1}{a^2}+2 \times a \times \frac{1}{a}=\left(a-\frac{1}{a}\right)^2$
So, the square root of $a^2+\frac{1}{a^2}+2$ is $a+\frac{1}{a}$.
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