Standard +0.8 This question requires expanding a quotient using the binomial theorem (including the non-trivial (1+3x)^(-1/2) expansion), multiplying series, identifying the validity condition from the more restrictive expansion, and then applying the result to approximate √22 by algebraic manipulation. It combines multiple techniques and requires insight to connect x=1/22 to √22, making it moderately harder than average.
Find the first three terms in the binomial expansion of \(\frac { 2 - x } { \sqrt { 1 + 3 x } }\) in ascending powers of \(x\). State the range of values of \(x\) for which the expansion is valid.
By writing \(x = \frac { 1 } { 22 }\) in your expansion, find an approximate value for \(\sqrt { 22 }\) in the form \(\frac { a } { b }\), where \(a , b\) are integers whose values are to be found.
Find the first three terms in the binomial expansion of $\frac { 2 - x } { \sqrt { 1 + 3 x } }$ in ascending powers of $x$. State the range of values of $x$ for which the expansion is valid.
By writing $x = \frac { 1 } { 22 }$ in your expansion, find an approximate value for $\sqrt { 22 }$ in the form $\frac { a } { b }$, where $a , b$ are integers whose values are to be found.
\hfill \mbox{\textit{WJEC Unit 3 2022 Q8}}