2015 MI P1 Q3
(i)
Expand $\frac{\sqrt[4]{1+3{{x}^{2}}}}{2+x}$ in ascending powers of $x$, up to and including the term in ${{x}^{2}}$.
[3]
(ii)
Find the set of values of $x$ for which the expansion in part (i) is valid.
[2]
(iii)
By substituting $x=-\frac{1}{4}$ and using your result in part (i), show that $\sqrt[4]{19}\approx \frac{p}{q}$, where $p$ and $q$ are integers to be determined.
[2]
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