- Let \(x\) be a solution of \(x^{2} + x + 1 = 0\)
- Since \(x\) is not 0, we can divide both sides by \(x\):
- \(x + 1 + \frac{1}{x} = 0\)

- Substitute \(x + 1 = -x^{2}\)
- \(\frac{1}{x} = x^{2}\)

- \(x = 1\)
- \(x = x^{3}\)

- \(3 = 0\)
- \(1^{2} + 1 + 1 = 0\)

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