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Solve for real x: |x² + x + 1| = |x² + x + 2|.

1. No real solution
2. x = 0 only
3. x = -1 only
4. All real x

Correct answer: No real solution

Solution

Both x² + x + 1 and x² + x + 2 have negative discriminants (1 - 4 < 0 and 1 - 8 < 0), so both are always positive. Then |A| = |B| reduces to A = B: x² + x + 1 = x² + x + 2 => 1 = 2, which is impossible. Hence there is no real solution.

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