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If the coefficients of x^2 and x^3 in the expansion of (3+k x)^9 are equal, then the value of k is

Option: 1

-\frac{9}{7}


Option: 2

\frac{9}{7}


Option: 3

\frac{7}{9}


Option: 4

None of these


Answers (1)

best_answer

\mathrm{T}_{r+1} \text { in }(3+\mathrm{kx})^9={ }^9 \mathrm{C}, 3^{9-r}(\mathrm{kx})^r

={ }^9 \mathrm{C}, 3^{9-r} k^r x^r 

Coefficient of x^r={ }^9 C_r 3^{9-r} k^r

Now coefficient of x^2 = coefficient of x^3

{ }^9 \mathrm{C}_2 3^{9-2} \mathrm{k}^2={ }^9 \mathrm{C}_3 3^{9-3} \mathrm{k}^3

\begin{aligned} & \Rightarrow 36 \times 3^7 k^2=84 \times 3^6 k^3 \\ & \Rightarrow 36=28 k \Rightarrow k=\frac{9}{7} \end{aligned}

Hence (B) is the correct answer.

 

Posted by

Suraj Bhandari

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