5.
$$f ( x ) = \frac { 10 } { \sqrt { 4 - 3 x } }$$
- Show that the first 4 terms in the binomial expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), are
$$A + B x + C x ^ { 2 } + \frac { 675 } { 1024 } x ^ { 3 }$$
where \(A , B\) and \(C\) are constants to be found. Give each constant in simplest form.
Given that this expansion is valid for \(| x | < k\)
- state the largest value of \(k\).
By substituting \(x = \frac { 1 } { 3 }\) into \(\mathrm { f } ( x )\) and into the answer for part (a),
- find an approximation for \(\sqrt { 3 }\)
Give your answer in the form \(\frac { a } { b }\) where \(a\) and \(b\) are integers to be found.
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