If the constant term in the binomial expansion of x 5 2 2 - 4 x l 9 is - 84 and the coefficient of x - 3 l is 2 α β where β < 0 is an odd number, then α l - β is equal to _____ .

Step-by-step solution

Given, The constant term in the binomial expansion of x 5 2 2 - 4 x l 9 is - 84 and the coefficient of x - 3 is 2 α β Now General Term of the binomial is given by, T r + 1 = C r 9 x 5 2 2 9 - r - 4 x l r = - 1 r C r x 45 2 - 5 r 2 - l r 2 3 - 9 Now for constant term 45 - 5 r - 2 l r = 0 ⇒ r = 45 5 + 2 l So, coefficient of constant term will be, - 1 9 × 9 C r 2 3 r - 9 = - 84 ⇒ r = 3 Now putting the value of r in r = 45 5 + 2 l we get, l = 5 Now coefficient of x - 3 l = x - 15 ⇒ 45 2