If x2 - 5√2x + 1 = 0, then what is the value of \(\frac{\left(x^3+\frac{1}{x}\right)}{x^2+1}\)?

1
\(\frac{12\sqrt{2}}{5}\)
2
\(\frac{24\sqrt{2}}{5}\)
3
\(\frac{26\sqrt{2}}{5}\)
4
\(\frac{18\sqrt{2}}{5}\)

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