The third term in the expansion of ${{\left( {{x}^{3}}+\frac{k}{{{x}^{m}}} \right)}^{5}}$, in desc

Question

The third term in the expansion of ${{\left( {{x}^{3}}+\frac{k}{{{x}^{m}}} \right)}^{5}}$, in descending powers of $x$, is the constant $160$. Find the values of $k$ and $m$.

Accepted Answer

$m = \frac{9}{2}$, $k = \pm 4$

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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