3.73: Binomial expansion beginning $b^{4} + 48b^{3}x$

0606/22/F/M/24 — Question 10 · 10 marks · Binomial

The expansion of

\left(a + \dfrac{x}{a}\right)^{n}

in ascending powers of

x

begins

b^{4} + 48b^{3}x

, where

n

a

and

b

are positive integers.

(a)

Show that

a^{\frac{n}{2} - 4} = \left(\dfrac{48}{n}\right)^{2}

[4]

(b)

Given also that the third term is

1056b^{2}x^{2}

, find the values of

n

a

and

b

[6]

3.73: Binomial expansion beginning b4+48b3xb^{4} + 48b^{3}xb4+48b3x