Solve cubic function

When x is a complex number, there are of course three roots.

You must be talking about real roots, but the solution must be based on complex roots.

If you only judge the solution, you can draw the first derivative, such as upstairs;

If you want to solve it, I'll teach you a way:

1 First, take the derivative of the left polynomial twice to make it 0, and get the inflection point.

Then transform x=t+ (inflection point) into the original equation and become a cubic equation without square (so that you will understand that if there is no square, you don't need to do these two steps), and leave x 3 alone on the left side of the equal sign.

Let t=s+p, and compare the two sides of the equation to get two equations: s 3+p 3 =? ，sp=？

Bring the second formula into the first formula and get a quadratic equation about S 3 or P 3. Solve it.

(Note: There is a qualitative analysis here, that is, what if the discriminant of quadratic equation is greater than or equal to 0?

Greater than 0 has a real root and a pair of yoke roots.

There are three real roots equal to 0.

Less than 0 has three different real roots)

According to symmetry, p 3 or s 3 (where s 3+p 3 =? )

4 (Because you may not know the solution of the root of a complex number, this step is especially prompted) Opening the root three times will always get three complex numbers.

5x=s+p+ (inflection point)

The only real root of your problem is (2/3)+[ (cube root) ((38/9)+(2/27)[ (quadratic root) (3233)]+[(cube root) ((38/9)-(2/27)]

Calculated by a calculator, it is about 2+2+20000. 38600 . 8686868686 1

Maybe you are not satisfied with the answer, but please tell your friends who want to know about this method that it is not a waste for me to call this method online for the first time. Thank you!