*a* and *b* be the smaller number and the larger number whose product is 1369\(\sqrt{2}\) and has a ratio of \(\sqrt{2}\) : 2. If \(\frac{a}{x^3}\) + \(\frac{1}{x^2}\) + \(\frac{1}{x}\) + 1 = 0, find \(x^3 + x^2 + x + b\).

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