$3x - \frac{1}{x} = 8$
$(3x - \frac{1}{x})^2 = 8^2$
$9x^2 - 2 * 3x * \frac{1}{x} + (\frac{1}{x})^2 = 64$
$9x^2 - 6 + \frac{1}{x^2} = 64$
$9x^2 + \frac{1}{x^2} = 64 + 6$
$9x^2 + \frac{1}{x^2} = 70$
Ответ: 70