If x+\(\frac{1}{15x}\) = 3
find \(\frac{1}{2}\)(9x3 + \(\frac{1}{{375x}^{3}}\)).
Answer & explanation
Correct answer: option 3
(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