Binomial theorem

Question

When the binomial theorem is used, the 12th term of (x/4 + b)¹⁴ is equal to -11648/x⁸.

Calculate the value of b in terms of x

Answer 1

Using the Binomial Theorem, the 12th term is ₁₄C₁₁(x/4)^14-11b¹¹ = -11648 / x⁸

₁₄C₁₁ = 14! / [(11! (14-11)!] = 364

So, 364 (x³ / 64)b¹¹ = -11648 / x⁸

x¹¹ / b¹¹ = -2048 = -2¹¹

So, x / b = -2

b = -x/2