Final answer:
The exhaustive values of x satisfying the equation (x - 1)(x² - 9)² = 0 are [-3, 1] U [3, 0). The correct answer is B. [-3, 1] U [3, 0).
Step-by-step explanation:
The set of exhaustive values of x satisfying the equation (x - 1)(x² - 9)² = 0 is:
A. [-3, 2) U [3, 0) - {1}
B. [-3, 1] U [3, 0)
C. (-∞, -3] U (2, 3]
D. (-∞, -3] U (1, 0)
The equation can be solved by factoring. In order for the product of two quantities to equal zero, at least one of the quantities must be equal to zero. So, we set each factor equal to zero:
(x - 1) = 0 or (x² - 9)² = 0
Solving these equations, we get x = 1, and x = ±3.
Therefore, the values of x that satisfy the equation are x = 1, x = 3, and x = -3.
The correct answer is B. [-3, 1] U [3, 0).