If the co-efficient of x 9 in α x 3 + 1 β x 11 and the co-efficient of x - 9 in α x - 1 β x 3 11 are equal, then ( α β ) 2 is equal to

Step-by-step solution

Given, The coefficient of x 9 in α x 3 + 1 β x 11 and the coefficient of x - 9 in α x - 1 β x 3 11 are equal, Now the r t h term of α x 3 + 1 β x 11 is given by = C r 11 · α 11 - r β r × x 3 11 - r - r So, for x 9 , 33 - 4 r = 9 ⇒ r = 6 Hence, coefficient of x 9 in α x 3 + 1 β x 11 = C 6 11 · α 5 β 6 Similarly, for coefficient of x - 9 in α x - 1 β x 3 11 = - C 5 11 · α 6 β 5 Now given both coefficient are equa