Question

Find a positive value of m for which the coefficient of $x^2$ in the expression $(1+x{)}^m$ is 6.

Answer 1

Here coefficient of $x^2$ in $(1+x{)}^m=m_{C_2}=6$

$\therefore \frac{m(m-1)}{2}=6$

$\Rightarrow m^2-m=12$

$\Rightarrow m^2-m-12=0$

$\Rightarrow m^2-4m+3m-12=0$

$\Rightarrow m(m-4)+3(m-4)=0$

$\Rightarrow (m-4)(m+3)=0$

Either m-4=0 or m+3=0

$\Rightarrow m=4$ or $m=-3$

So positive value of m is 4.