The fifth term in the expansion of ${{\left( {{x}^{2}}+\frac{k}{{{x}^{m}}} \right)}^{8}}$, in desc

Question

The fifth term in the expansion of ${{\left( {{x}^{2}}+\frac{k}{{{x}^{m}}} \right)}^{8}}$, in descending powers of $x$, is the constant $5670$. Find the values of $k$ and $m$.

Accepted Answer

$m = 2$, $k = \pm 3$

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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