Could I please know how to expand:
$$\sqrt{4-3x^2}$$
I simplified it to $\sqrt{1-\frac34x^2}$ but the question is if I let $x = x^2$, what will the coefficient of, say $x^5$ or $x^{10}$ be in the expansion?
2026-03-29 04:48:58.1774759738
Series expansion of square root function
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HINT :
Rewrite \begin{align} \sqrt{4-3x^2}&=(4-3x^2)^\frac12\\ &=\left(4\left(1-\frac34x^2\right)\right)^\frac12\\ &=2\left(1-\frac34x^2\right)^\frac12\\ &=2\left(1-\left(\frac{\sqrt3}{2}x\right)^2\right)^\frac12\\ \end{align} Now, let $y=\dfrac{\sqrt3}{2}x$ and use binomial series for $\left(1-y^2\right)^\frac12$.