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if the exppansion of (1+x)^m(1-x)^n ,the coefficients of x and x^2 are 3 and -6 respectively then find the value of m and n?

if the exppansion of (1+x)^m(1-x)^n ,the coefficients of x and x^2 are 3 and -6 respectively then find the value of m and n? 

Grade:11

1 Answers

Jayesh Arun Kadam
34 Points
10 years ago

(1+x)m(1-X)n

=(1+mC1X + mC2X2+....mCmXm) (1-nC1X+nC2X2-....+nCnXn)

For coefficient of  X  => (mC1 - nC1) =3

m-n=3

??For coefficient of X2  => (mC2 + nC2 - mC1.nC1)=-6

m(m-1)/2 + n(n-1)/2 -mn=-6

 

By solving these two eqns we get

n=9  m=12

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