Tìm x: x^3 - 8x + 1 = 0

To solve the equation x^3 - 8x + 1 = 0, we can use the Rational Root Theorem to find possible rational roots. The Rational Root Theorem states that if a polynomial equation has a rational root p/q, where p is a factor of the constant term (in this case, 1) and q is a factor of the leading coefficient (in this case, 1), then p/q is a possible rational root.

The factors of 1 are ±1, and the factors of 1 are ±1. Therefore, the possible rational roots are ±1.

We can test these possible roots by substituting them into the equation:

For x = 1: (1)^3 - 8(1) + 1 = 1 - 8 + 1 = -6
For x = -1: (-1)^3 - 8(-1) + 1 = -1 + 8 + 1 = 8

Since neither x = 1 nor x = -1 satisfy the equation, there are no rational roots for x^3 - 8x + 1 = 0.

To find the other roots, we can use numerical methods such as graphing or using a calculator.