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