MCQ
The square root of $\frac{a^2}{4}+\frac{1}{a^2}-\frac{1}{a}+\frac{a}{2}-\frac{3}{4}$ is
- ✓$\frac{a}{2}-\frac{1}{a}+\frac{1}{2}$
- B$\frac{a}{2}+\frac{2}{a}-1$
- C$\frac{a}{2}+\frac{1}{a}-\frac{1}{2}$
- D$\frac{a}{2}-\frac{2}{a}-\frac{1}{2}$
✓
Answer
Correct option: A.
$\frac{a}{2}-\frac{1}{a}+\frac{1}{2}$
(a)
$\frac{a^2}{4}+\frac{1}{a^2}-\frac{1}{a}+\frac{a}{2}-\frac{3}{4}$
$=\left(\frac{a}{2}\right)^2+\left(-\frac{1}{a}\right)^2+\left(\frac{1}{2}\right)^2+2\left(\frac{a}{2}\right)\left(\frac{1}{2}\right)+2\left(-\frac{1}{a}\right)\left(\frac{1}{2}\right)+2\left(\frac{a}{2}\right)\left(-\frac{1}{a}\right)=\left(\frac{a}{2}-\frac{1}{a}+\frac{1}{2}\right)^2$
Hence, required square root is $\left(\frac{a}{2}-\frac{1}{a}+\frac{1}{2}\right)$
$\frac{a^2}{4}+\frac{1}{a^2}-\frac{1}{a}+\frac{a}{2}-\frac{3}{4}$
$=\left(\frac{a}{2}\right)^2+\left(-\frac{1}{a}\right)^2+\left(\frac{1}{2}\right)^2+2\left(\frac{a}{2}\right)\left(\frac{1}{2}\right)+2\left(-\frac{1}{a}\right)\left(\frac{1}{2}\right)+2\left(\frac{a}{2}\right)\left(-\frac{1}{a}\right)=\left(\frac{a}{2}-\frac{1}{a}+\frac{1}{2}\right)^2$
Hence, required square root is $\left(\frac{a}{2}-\frac{1}{a}+\frac{1}{2}\right)$
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