Hai
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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