Question 4 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2008
Session	June
Topic	Generalised Binomial Theorem
Type	Factoring out constants before expansion

1. Obtain the binomial expansion of \(( 1 - x ) ^ { \frac { 1 } { 4 } }\) up to and including the term in \(x ^ { 2 }\).
2. Hence show that \(( 81 - 16 x ) ^ { \frac { 1 } { 4 } } \approx 3 - \frac { 4 } { 27 } x - \frac { 8 } { 729 } x ^ { 2 }\) for small values of \(x\).
Use the result from part (a)(ii) to find an approximation for \(\sqrt [ 4 ] { 80 }\), giving your answer to seven decimal places.