If in the expansion of 1 + x m 1 - x n , the coefficients of x and x 2 are 3 and – 6 respectively, then the value of m is m , n ∈ N

Question

If in the expansion of 1 + x m 1 - x n , the coefficients of x and x 2 are 3 and – 6 respectively, then the value of m is m , n ∈ N, 6, 9, 12, 24

MARKS App · Accepted Answer

Given expansion = 1 + m C 1 x + m C 2 x 2 + . . . . 1 - n C 1 x + n C 2 x 2 - . . . . Coefficient of x 2 = - n C 1 + m C 1 = m - n = 3 Coefficient of x 2 = n C 2 - m C 1 m C 1 + m C 2 = n n - 1 2 - m n + m m - 1 2 ⇒ n n - 1 2 - m n + m m - 1 2 = - 6 n = m – 3 ⇒ m - 3 m - 4 2 + m m - 1 2 - m m - 3 = - 6 ⇒ m 2 - 7 m + 12 + m 2 - m - 2 m 2 + 6 m = - 1 2 ⇒ - 2 m = - 24 ⇒ m = 1 2

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