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Question
If in the expansion of (1+x)m(1−x)n, the coefficient of x and x2 are 3 and −6 respectively, then m is
If in the expansion of (1+x)m(1−x)n, the coefficient of x and x2 are 3 and −6 respectively, then m is
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Solution
The correct option is C 12
It can be written (1+x)m(1−x)n as
={1+mx+m(m−1)2!x2+....}{1−nx+n(n−1)2!x2−....}=1+(m−n)x+[n2−n2−mn+m2−m2]x2+.....
Given, m−n=3 or n=m−3
and n2−n2−mn+m2−m2=−6
Thus (m−3)(m−4)2−m(m−3)+m2−m2=−6
⇒−2m+24=0
⇒ m=12
It can be written (1+x)m(1−x)n as
={1+mx+m(m−1)2!x2+....}{1−nx+n(n−1)2!x2−....}
=1+(m−n)x+[n2−n2−mn+m2−m2]x2+.....
Given, m−n=3 or n=m−3
and n2−n2−mn+m2−m2=−6
Thus (m−3)(m−4)2−m(m−3)+m2−m2=−6
⇒−2m+24=0
⇒ m=12
Given, m−n=3 or n=m−3
and n2−n2−mn+m2−m2=−6
Thus (m−3)(m−4)2−m(m−3)+m2−m2=−6
⇒−2m+24=0
⇒ m=12
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