If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of 2 x 3 + 3 x 10 is 5 10 - β · 3 9 , then β is equal to _____.

Step-by-step solution

Given, Binomial expression 2 x 3 + 3 x 10 , so its n t h term is given by, T r + 1 = C r 10 2 x 3 10 - r 3 x r = C r 10 2 10 - r 3 r x 30 - 4 r Now putting r = 0 , 1 , 2 , . . . . . 7 and adding all term we get 2 x 3 + 3 x 10 = C 0 10 2 10 3 0 x 30 + C 1 10 2 9 3 1 x 26 . . . . . . . . . . . . . . C 7 10 2 3 3 7 x 2 + C 8 10 2 2 3 8 1 x 2 . . . . 2 x 3 + 3 x 10 - C 8 10 2 2 3 8 1 x 2 . . . . . . . = C 0 10 2 10 3 0 x 30 + C 1 10 2 9 3 1 x 26 . . . . . . . . . . . . . . C 7 10 2 3 3 7 x 2 Put x = 1 both side we get,