If the coefficients of x 2 and x 3 in the expansion of \((3+\text{ax})^{9}\) are the same, then the value of…

If the coefficients of x2 and x3 in the expansion of \((3+\text{ax})^{9}\) are the same, then the value of a is:

  1. \(\frac{9}{7}\)

  2. \(\frac{7}{9}\)

  3. \(-\frac{9}{7}\)

  4. \(-\frac{7}{9}\)

Solution

Solution:

Coefficients of x2 = Coefficients of x3

\({^\text{9}}\text{C}_{\text{2}}\times3^{9-2}\text{a}^{2}={^\text{9}}\text{C}_{\text{3}}\times3^{9-3}\ \text{a}^{3}\)

\(\Rightarrow \text{a}=\frac{{^\text{9}}\text{C}_{\text{2}}}{{^\text{9}}\text{C}_{\text{3}}}\times3\)

\(=\frac{9!\times3!\times6!\times3}{2!\times7!\times9!}\)

\(=\frac{9}{7}\)

Asked in: RDSHARMA

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