Question

find a positive value of m for which the coefficient of x square in the expansion of ( 1+x)m is 6.?

Answer 1

Please see the attachment

Answer 2

Coefficients of x^2 in the equation ( 1+x)^m is C( m, 2) .

According to the problem,

C (m, 2) = 6

m(m-1)/2! = 6

m^2 - m = 12

m^2 - m- 12 = 0

m^2 - 4m + 3m -12 =0

m(m-4) + 3(m-4)= 0

(m-4) (m+3) =0

m = 4 since m ≠ -3

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