If the term without x in the expansion of x 2 3 + α x 3 22 is 7315 , then α is equal to _____ .

Step-by-step solution

General term in the binomial expansion of x 2 3 + α x 3 22 is T r + 1 = C r 22 x 2 3 22 - r α x 3 r ⇒ T r + 1 = C r 22 x 44 - 11 r 3 α r For term independent of x , 44 - 11 r 3 = 0 ⇒ r = 4 So, T 5 = C 4 22 α 4 = 7315 ⇒ 22 ! 4 ! × 18 ! α 4 = 7315 ⇒ 7315 α 4 = 7315 ⇒ α 4 = 1 ⇒ α = 1