X³-9x = 0

To solve the equation \( x^3 - 9x = 0 \), we can start by factoring the expression. 1. Factor out \( x \): \[ x(x^2 - 9) = 0 \] 2. Recognize that \( x^2 - 9 \) is a difference of squares, which can be factored further: \[ x(x - 3)(x + 3) = 0 \] 3. Set each factor equal to zero: - \( x = 0 \) - \( x - 3 = 0 \) ⟹ \( x = 3 \) - \( x + 3 = 0 \) ⟹ \( x = -3 \) Thus, the solutions to the equation \( x^3 - 9x = 0 \) are: \[ x = 0, \quad x = 3, \quad x = -3 \]