Q. The expansion of $\frac{1}{{(4 - 3x)}^{\frac{1}{2}}}$ by Only One Correct Option will be valid, if
A) $x < 1$
B) $|x| < 1$
C) $- \frac{2}{\sqrt{3}} < x < \frac{2}{\sqrt{3}}$
D) None of these
Explanation
(d)
The given expression of $\frac{1}{{(4 - 3x)}^{\frac{1}{2}}}$ can be rewritten as
$4^{\frac{- 1}{2}}\left( 1 - \frac{3}{4}x \right)^{\frac{- 1}{2}}$ and it is valid only when $\left| \frac{3}{4}x \right| < 1$
$\Rightarrow \ - \frac{4}{3} < x < \frac{4}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.