If the co-efficient of x^9 in ( alpha x^3 + 1 / beta x )^11 and the co-efficient of x^-9 in ( alpha x - 1 / beta x^3 )^11 are equal, then (alphabeta)^2 is equal to ___________.

Coefficient of x^9 in (alpha x^3+(1 / beta x))= ^11 C_6 * fracalpha^5beta^6 Because Both are equal Therefore frac11C_6 * fracalpha^5beta^6=-frac11C_5 * fracalpha^6beta^5 => (1 / beta)=-alpha => alpha beta=-1 => (alpha beta)^2=1

If the coefficient of x9 in alpha x3 1 beta x 11 and th... | null (Mathematics)

Coefficient of

\mathrm{x}^{9}

\left(\alpha x^{3}+\frac{1}{\beta x}\right)={ }^{11} C_{6} \cdot \frac{\alpha^{5}}{\beta^{6}}

\because

Both are equal

\therefore \frac{11}{C_{6}} \cdot \frac{\alpha^{5}}{\beta^{6}}=-\frac{11}{C_{5}} \cdot \frac{\alpha^{6}}{\beta^{5}}

\Rightarrow \frac{1}{\beta}=-\alpha

\Rightarrow \alpha \beta=-1

\Rightarrow(\alpha \beta)^{2}=1

Explanation

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