Question

If p is a real number and if the middle term in the expansion of  \[\left( \frac{p}{2} + 2 \right)^8\] is 1120, find p.

 

 

Answer 1

In the binomial expansion of \[\left( \frac{p}{2} + 2 \right)^8\] , we observe that  \[\left( \frac{8}{2} + 1 \right)^{th}\]  i.e., 5^th term is the middle term.

It is given that the middle term is 1120.

\[\therefore T_5 = 1120\]

\[ \Rightarrow^8 C_4 \left( \frac{p}{2} \right)^{8 - 4} \left( 2 \right)^4 = 1120\]

\[ \Rightarrow p^4 = 16\]

\[ \Rightarrow p = \pm 2\] 

Hence, the real values of p is \[\pm 2\]