Expand $\frac{1}{{(4 - 3 x^{2})}^{\frac{1}{3}}}$ . Find the range of values of $x$ for which the expansion is applicable.

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Solution

We need to expand $\frac{1}{(4 - 3 x^{2})^{\frac{1}{3}}}$
For it to be applicable
$\Rightarrow$ $(4 - 3 x^{2})$ $> 0$
$\Rightarrow$ $(3 x^{2} - 4) < 0$
$\Rightarrow$ $x^{2} < \frac{4}{3}$
$\Rightarrow$ $- \frac{2}{\sqrt{3}} < x < \frac{2}{\sqrt{3}}$
Thus $x$ $\in$ $(\frac{- 2}{\sqrt{3}}, \frac{2}{\sqrt{3}})$

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