Question

how to solve for x for cubic root of x + 1

Answer 1

To solve for x in the equation "cubic root of x + 1," we need to isolate x on one side of the equation. Here's how you can do it:

1. Start with the equation: ³√(x + 1).
2. Cube both sides of the equation to eliminate the cube root: (³√(x + 1))³ = x.
This simplifies to: x + 1 = x^3.
3. Rearrange the equation so that one side is zero: x^3 - x - 1 = 0.
4. At this point, you can either factor the equation or use numerical methods such as Newton's method to approximate the roots.

If you want to factor the equation:
5. By inspection, x = -1 is a root of the equation.
6. Use polynomial long division or synthetic division to divide (x + 1) by (x^3 - x - 1) to find the other quadratic factor.
This gives you: (x^3 - x - 1) / (x + 1) = x^2 - x + 1.
7. Solve x^2 - x + 1 = 0 by factoring or using the quadratic formula.
This will give you two complex roots.

Hence, the solutions to the equation cubic root of x + 1 = x are x = -1 and two complex roots from solving x^2 - x + 1 = 0.