If the coefficient of x 7 in a x - 1 b x 2 13 and the coefficient of x - 5 in a x + 1 b x 2 13 are equal, then a 4 b 4 is equal to:

Step-by-step solution

Given, The coefficient of x 7 in the expansion of a x 2 - 1 b x 13 is equal to the coefficient of x - 5 in a x + 1 b x 2 13 . We know that, the general term T r + 1 in the expansion a + b n is T r + 1 = C r n a n - r b r Applying to a x - 1 b x 2 13 , we get T r + 1 = C r 13 a x 13 - r - 1 b x 2 r ⇒ T r + 1 = - 1 r × C r 13 a 13 - r x 13 - 3 r b - r Therefore, 13 - 3 r = 7 ⇒ r = 2 for coefficient of x 7 . Thus, T 3 = C 2 13 a 11 b 2 Similarly, applying to a x + 1 b x 2 13 , we get T r + 1 = C r 13