Let a and b be two nonzero real numbers. If the coefficient of x 5 in the expansion of a x 2 + 70 27 b x 4 is equal to the coefficient of x - 5 in the expansion of a x - 1 b x 2 7 , then the value of 2 b is

Step-by-step solution

Given, The coefficient of x 5 in a x 2 + 70 27 b x 4 is equal to coefficient of x - 5 in a x - 1 b x 2 7 , Now finding the coefficient of x 5 in a x 2 + 70 27 b x 4 we get, T r + 1 = C r 4 a x 2 4 - r · 70 27 b x r ⇒ T r + 1 = C r 4 a 4 - r · 70 27 b r · x 8 - 2 r - r So, 8 - 2 r - r = 5 ⇒ r = 1 So, T 2 = C 1 4 a 3 · 70 27 b · x 5 Now finding the coefficient of x - 5 in a x - 1 b x 2 7 we get, T r + 1 = C r 7 a x 7 - r · 1 b x 2 r ⇒ T r + 1 = C r 7 a 7 - r · 1 b