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If the coefficents of x^(2) and x^(3) i...

If the coefficents of `x^(2) and x^(3)` in the expansion of `(3+px)^(9)` are the same then prove that `p= 9/7`.

Text Solution

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`T_(r+1)= .^(9)C_(r)3^((9-1)) xx(px)^(r) = .^(9)C_(r)3^((9-r))* p ^(r)x^(r).`
`" Coeff. of " x^(2) = " coeff.of " x^(3) rArr .^(9) C_(2) xx 3^(7) xx p^(2) = .^(9) C _(3) xx 3^(6) xx p^(3).`
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