If in the expansion $$(1+x)m(1$$−$$x)n$$, the coefficient of x and $$x2$$ are $$3$$ and $$-6$$ respectively then m is

Question

If in the expansion $$(1+x)m(1$$−$$x)n$$, the coefficient of x and $$x2$$ are $$3$$ and $$-6$$ respectively then m is

Infinity Learn · Accepted Answer

We have, (1+x)m(1$$−$$x)n$$  $$=$$ $$mC0+mC1x+mC2x2+$$…$$+mCmxm$$× $$nC0$$−$$nC1x+nC2x2$$…..$$+($$−$$1)nnCnxn=mC0nC0$$− $$mC0nC1$$−$$nC0mC1x+$$ $$mC0nC2+nC0mC2$$−$$mC1$$⋅$$nC1x2+$$…..It is given that the coefficients of x and  x $$2$$ in the expansion $$(1+x)m(1$$−$$x)m$$ are $$3$$ and $$-6$$ respectively  ∴− $$mC0nC1$$−$$nC0mC1=3and$$ ,  $$mC0nC2+nC0mC2$$−$$mC1nC1=$$−$$6$$ ⇒m−$$n=3$$ and $$n(n$$−$$1)+m(m$$−$$1)−$$2mn=$$−$$12$$ ⇒m−$$n=3$$ and $$(m$$−$$n)2$$−$$(m+n)=$$−$$12$$ ⇒m−$$n=3$$ and  $$m+n=21$$ ⇒$$m=12$$,$$n=9$$

If in the expansion $(1 + x)^{m} (1 - x)^{n}$ , the coefficient of $x$ and $x^{2}$ are 3 and -6 respectively then $m$ is

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If in the expansion (1+x)m(1−x)n, the coefficient of x and x2 are 3 and -6 respectively then m is

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If in the expansion $(1 + x)^{m} (1 - x)^{n}$ , the coefficient of $x$ and $x^{2}$ are 3 and -6 respectively then $m$ is