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General Term of Binomial Expansion

If x is a p...

Question

If $x$ is a positive integer satisfying $x^{7} = k$ and $x^{9} = m$ , which of the following must be equal to $x^{11}$ ?

\frac{m^{2}}{k}

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m^{2} - k

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m^{2} - 7

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2 k - \frac{m}{3}

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k + 4

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Solution

The correct option is A $\frac{m^{2}}{k}$
Given, $x^{7} = k, x^{9} = m$
$x^{11} = \frac{x^{18}}{x^{7}}$
Put the given values, we get
$x^{11} = \frac{m^{2}}{k}$

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