If $k^4+\frac{1}{k^4}=194$, then what is the value of $k^3+\frac{1}{k^3}$?

42 52 36 18

52

If x4 + \(\frac{1}{x^4}\) = a then x2 + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\) = b and x + \(\frac{1}{x}\) = \(\sqrt {b + 2}\)  $k^4+\frac{1}{k^4}=194$ $k^3+\frac{1}{k^3}$ = ? k2 + \(\frac{1}{k^2}\) = \(\sqrt {194 + 2}\) = 14 and k + \(\frac{1}{k}\) = \(\sqrt {14 + 2}\) = 4 $k^3+\frac{1}{k^3}$ = 43 - 4 × 3 = 52