Question

If p is a real number and if the middle term in the expansion of (p/2 + 2)^8 is 1120, find p.

Answer 1

Value of p is 2.

Step-by-step explanation:

The expansion will have (8 + 1) = 9 terms.

Thus the middle term is the (9 + 1)/2 = 5th term of the expansion.

∴ 5th term = ⁸C₄ * (p/2)⁸⁻⁴ * 2⁴

= 70 * (p/2)⁴ * 2⁴

= 70 * (p⁴ / 2⁴) * 2⁴

= 70 * p⁴

By the given condition,

70 * p⁴ = 1120

or, p⁴ = 1120/70

or, p⁴ = 16

or, p⁴ = 2⁴

This gives p = 2

Note: Since p is a real number, we take only the real value of p (= 2) and exclude other complex values of p.