Так то да, но для понимания решения такие нюансы несущественны.

Мой запрос в chat gpt "x^3-7x+6=0 provide a solution".

Её ответ:

To solve the equation x^3 - 7x + 6 = 0, we can start by factoring the left-hand side of the equation.

One way to factor this equation is to factor out a greatest common factor (GCF) from the left-hand side. In this case, the GCF is 1, so we can write:

x^3 - 7x + 6 = (x-1)(x^2 + x - 6) = 0

Now we have a quadratic equation in the form of (x-1) (x^2 + x - 6) = 0. Using the zero product property, we know that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, either x-1 = 0 or x^2 + x - 6 = 0.

Solving for x-1 = 0, we find that x = 1.

To solve the quadratic equation x^2 + x - 6 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a

where a = 1, b = 1, and c = -6.
Therefore, the solutions are
x = (-1 ± √(1 + 24))/2 = (-1 ± √25)/2 = (-1 ± 5)/2 = -3 or 2

So the solutions to the original equation are x = 1, -3 and 2

In general for x^3-ax^2-bx-c=0, one method to find the solutions is using polynomial roots that is factorisation. But it may also have complex solutions, it depends on the polynomial degree, the value of a,b,c.