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Problem 10 - Olympiad
Solve the equation x^3 - 6x^2 + 11x - 6 = 0.
A. x = 1, x = 2, x = 3
B. x = -1, x = -2, x = -3
C. x = 0, x = 1, x = 2
D. x = 1, x = -2, x = 3
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Correct: A
The given equation is a cubic equation. To solve for x, we first try to factor the left-hand side. We can factor the equation as (x - 1)(x - 2)(x - 3) = 0. Setting each factor equal to zero gives the solutions x = 1, x = 2, and x = 3.