<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Expand $\frac{\sqrt[4]{1+3{{x}^{2}}}}{2+x}$ in ascending powers of $x$, up to and including the term in ${{x}^{2}}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the set of values of $x$ for which the expansion in part (i) is valid.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">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.</span></div><p style="text-align: right;">[2]</p></li></ol>

Expand $\frac{\sqrt[4]{1+3{{x}^{2}}}}{2+x}$ in ascending powers of $x$, up to and including the term in ${{x}^{2}}$.

Find the set of values of $x$ for which the expansion in part (i) is valid.

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.

2015 MI P1 Q3

2015 MI P1 Q3

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