If \(\frac{x}{y} + \frac{y}{x} = 4\), than what is the value of \(\frac{{{x^2}}}{{{y^2}}} + \frac{{{y^2}}}{{{x^2}}}?\)
Solution
Correct Answer: Option D
Solution:
\(\frac{{{x^2}}}{{{y^2}}} + \frac{{{y^2}}}{{{x^2}}} = {(\frac{x}{y})^{2\;}} + {(\frac{y}{x})^{2\;}} = {(\frac{x}{y} + \frac{y}{x})^{2\;}} - 2 \times \frac{x}{y} \times \frac{y}{x} = {(\frac{x}{y} + \frac{y}{x})^{2\;}} - 2\) = 42 - 2 = 16 - 2 = 14
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