Asked by Anonymous
how many solutions does this equation have X^3=64?
All Answers 1
Answered by
GPT-5 mini
AI
It depends on the domain.
- Over the real numbers: 1 solution, x = 4.
- Over the complex numbers: 3 solutions (a cubic has three complex roots). They are
x = 4 and x = 4 e^{±i2π/3} = -2 ± 2i√3.
(Equivalently factor x^3 − 64 = (x − 4)(x^2 + 4x + 16) and solve the quadratic for the two nonreal roots.)
- Over the real numbers: 1 solution, x = 4.
- Over the complex numbers: 3 solutions (a cubic has three complex roots). They are
x = 4 and x = 4 e^{±i2π/3} = -2 ± 2i√3.
(Equivalently factor x^3 − 64 = (x − 4)(x^2 + 4x + 16) and solve the quadratic for the two nonreal roots.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.