If 5x + \(\frac{1}{3x}\)= 4 find 9x² + \(\frac{1}{{25x }^{2 }}\)

\(\frac{114}{25}\)

5x + \(\frac{1}{3x}\) = 4

Multiply by \(\frac{3}{5}\) in equation

\(\frac{3}{5}\) (5x + \(\frac{1}{3x}\)) = 4 \(\times \) \(\frac{3}{5}\)

3x + \(\frac{1}{5x}\) = \(\frac{12}{5}\)

By squaring on both sides

9x² + \(\frac{1}{{25x }^{ 2}}\) + 2\(\times \) 3 \(\times \) \(\frac{1}{5}\) = \(\frac{144}{25}\)

9x² + \(\frac{1}{{25x }^{ 2}}\) = \(\frac{144}{25}\) - \(\frac{6}{5}\) = \(\frac{114}{25}\)