If in the expansion of (1+x)m(1−x)n, the coefficients of r and x are 3 and -6 respectively, the values of m and n are

We have,Coefficient of x in (1+x)m(1−x)n=mC1−nC1and coefficient of x in (1+x)m(1−x)n=mC2−mC1nC1+nC2According to the question,  mC1−nC1=3⇒m−n=3----iand mC2−mC1nC1+nC2=−6⇒m(m−1)2−mn+m(n−1)2=−6⇒(m−n)2−(m+n)=−12⇒9−(m+n)=−12      [from Eq. (6)] or m+n=21----iiFrom Eqs. (i) and (ii), we get m =12 and n = 9