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Solve the equation (x² - 3x)(x² - 3x + 2) + 1 = 0.

1. x = (3 + sqrt(5))/2
2. x = (3 - sqrt(5))/2
3. x = (3 +- sqrt(5))/2
4. x = (1 +- sqrt(5))/2

Correct answer: x = (3 +- sqrt(5))/2

Solution

Let u = x² - 3x. Then u(u + 2) + 1 = u² + 2u + 1 = (u + 1)² = 0, so u = -1. Hence x² - 3x + 1 = 0, giving x = (3 +- sqrt(9 - 4))/2 = (3 +- sqrt(5))/2.

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