X3-81x=0

To solve the equation \( x^3 - 81x = 0 \), we can factor it. First, we can factor out an \( x \):

\[ x(x^2 - 81) = 0 \]

Next, we can recognize that \( x^2 - 81 \) is a difference of squares, which can be factored further:

\[ x(x - 9)(x + 9) = 0 \]

Now, we can set each factor equal to zero to find the solutions:

1. \( x = 0 \)
2. \( x - 9 = 0 \) → \( x = 9 \)
3. \( x + 9 = 0 \) → \( x = -9 \)

Thus, the solutions to the equation \( x^3 - 81x = 0 \) are:

\[ x = 0, \quad x = 9, \quad x = -9 \]