If in the expansion of ( 1 + x ) m ( 1 – x ) n the coefficients of x and x 2 are – 2 and – 6 respectively, then the value of m + n is

Question

If in the expansion of ( 1 + x ) m ( 1 – x ) n the coefficients of x and x 2 are – 2 and – 6 respectively, then the value of m + n is, 12, 14, 16, 18

MARKS App · Accepted Answer

( 1 + x ) m ( 1 – x ) n = 1 + m x + m m – 1 2 x 2 + . . . 1 – n x + n n – 1 2 x 2 + . . . ⇒ m - n = - 2 and m ( m – 1 ) 2 + n ( n – 1 ) 2 – m n = – 6 ⇒ m = 7 a n d n = 9

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