Correct Answer: Option C

Explanation

Using common ratios

\(\frac{\text{x}}{\frac{16}{9}}\) = \(\frac{1}{\text{x}}\)

x\(^2\) = \(\frac{16}{9}\)

 x = \(\frac{4}{3}\)

If x = \(\frac{4}{3}\)

Then, the common ratio =  \(\frac{3}{4}\)

y = ar\(^3\) = \(\frac{16}{9}\) x (\(\frac{3}{4}\))\(^3\)

y =  \(\frac{16}{9}\) x \(\frac{27}{64}\) = \(\frac{3}{4}\)

Therefore, the product of x and y = \(\frac{4}{3}\) x \(\frac{3}{4}\) = 1

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