Hai

<Puzzle>

Let x be a solution to the equation x² + x + 1 = 0.

x² = − x − 1 (Moving x + 1 to R.H.S.)

x = − 1 − 1 / x (Dividing x)

Note it is legal division as x ≠ 0 is given by provided equation

Substitute x = − 1 − 1 / x back in for x the original equation

x² + ( −1 − 1 / x ) + 1 = 0

x² = 1 / x (Simplify)

x³ = 1 (Multiplying x on both sides)

x = 1 (Solving the cube root)

Substitute x = 1 into the original equation:

(1)² + 1 + 1 = 0

3=0

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