If $8k^{6} + 15k^{3} - 2 = 0$, then the positive value of $\left(k + \frac{1}{k}\right)$ is:

$2\frac{1}{2}$ $2\frac{1}{8}$ $8\frac{1}{2}$ $8\frac{1}{8}$

$2\frac{1}{2}$

8k6 + 15k3 – 2 = 0 Let, k3 = m So, 8m2 + 15m - 2 = 0 = 8m2 + 16m - m - 2 = 0 = 8m (m + 2) - 1 (m + 2) = 0 = (8m - 1) (m + 2) = 0 = 8m - 1 = 0  m = \(\frac{1}{8}\) k3 = \(\frac{1}{8}\) k =  \(\frac{1}{2}\) $\left(k + \frac{1}{k}\right)$ = \(\frac{1}{2}\) + 2 = $2\frac{1}{2}$