Question

List the members of these sets:
(a) x ∈R, x³ = x

Answer 1

The set x contains the real number solutions to the equation x³ - x = 0, which are 0, 1, and -1.

Step-by-step explanation:

To list the members of the set x , we need to solve the equation for x in the real numbers (R). This equation can be rewritten as x³ - x = 0. To solve this cubic equation, we can factor out an x, yielding x(x² - 1) = 0. This gives us two factors: x and (x² - 1), which can be further factorized to (x - 1)(x + 1) as it resembles the difference of squares. So our factors are x, (x - 1), and (x + 1).

Setting each factor equal to zero gives us the solutions for x. Therefore, the solutions are:

• x = 0
• x = 1
• x = -1

Hence, the members of the set are 0, 1, and -1.