Question

If $(1+ax{)}^n=1+8x+24x^2+.....,$ then the values of a and n are equal to

• A. 2, 4
• B. 2, 3
• C. 3, 6
• D. 1, 2

Answer 1

The correct option is A 2, 4

We know ,

$\Rightarrow {(1+ax)}^n=1+8x+24x^2+\_\_\_\_$

By using binomial -

$\Rightarrow {(a+x)}^n=a^n+{{}^{n}C}_1{a}^{n-1}x+{{}^{n}C}_2{a}^{n-2}{x}^2+\_\_\_$

So,

$\Rightarrow na=8$

$\Rightarrow n^2{a}^2=64$

And $\frac{n(n-1)}{2}{a}^2=24$

$\Rightarrow \frac{2n}{n-1}=\frac{8}{3}$

$6n=8n-8$

$\Rightarrow n=4$

So, $na=8$

$\Rightarrow a=2.$

Hence, the answer is $2,4.$