If (1+ax)n = 1 + 8x + 24 x2 + ......, then the value of a and n is

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Question

If

(1 + a x)^{n}

= 1 + 8x + 24

x^{2}

+ ......, then the value of a and n is

Options:

A . 2, 4

B . 2, 3

C . 3, 6

D . 1, 2

Answer: Option A
:
A
As given

(1 + a x)^{n}

= 1 + 8x + 24

x^{2}

+ .........
⇒ 1 +

\frac{n}{1}

ax +

\frac{n (n - 1)}{1.2}

a^{2} x^{2}

+ ......... = 1 + 8x + 24

x^{2}

+ ...........
⇒na = 8,

\frac{n (n - 1)}{1.2}

a^{2}

= 24⇒ na(n-1)a = 48
⇒8(8 -a) = 48⇒ 8 - a = 6⇒ a = 2⇒ n = 4.

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