If x+\(\frac{1}{15x}\) = 3

find \(\frac{1}{2}\)(9x³ + \(\frac{1}{{375x}^{3}}\)).

118.8

(x+\(\frac{1}{15x}\))³ = x³ + \(\frac{1}{{3375x}^{3}}\) + 3 \(\times \) x \(\times \) \(\frac{1}{15x}\) (x+\(\frac{1}{15x}\)) = (3)³

x³ + \(\frac{1}{{3375x}^{3}}\) + \(\frac{3}{5}\) = 27

x³ + \(\frac{1}{{3375x}^{3}}\) = 27 - \(\frac{3}{5}\) = \(\frac{132}{5}\)

Multiply eq. by 9 and divide by 2.

\(\frac{1}{2}\) (9x³ + \(\frac{1}{{375x}^{3}}\))  = \(\frac{132}{5}\) \(\times \) \(\frac{9}{2}\) = 118.8