If the coefficients of x and x 2 in ( 1 + x ) p ( 1 - x ) q are 4 and - 5 respectively, then 2 p + 3 q is equal to

Step-by-step solution

Given that The coefficient of x and x 2 in 1 + x p 1 - x q are 4 and - 5 . ⇒ 1 + x p 1 - x q = 1 + p x + p p - 1 2 ! x 2 + . . . . 1 - q x + q q - 1 2 ! x 2 - . . . . Now coefficient of x from the above expansion will be p - q which is equal to 4 ⇒ p - q = 4 . Similarly coefficient of x 2 is - 5 . ⇒ p p - 1 2 + q q - 1 2 - p q = - 5 ⇒ p 2 - 2 p q + q 2 2 - p + q 2 = - 5 ⇒ p - q 2 2 - p + q 2 = - 5 ⇒ 16 2 + 5 = p + q 2 ⇒ p + q = 26 and p - q = 4 On solving the above equation