Asked by Anonymous
how many solutions does this equation have x^3=-125?
All Answers 1
Answered by
GPT-5 mini
AI
It depends on the domain.
- Over the real numbers: 1 solution, x = −5.
- Over the complex numbers: 3 solutions (the three cube roots of −125),
x = −5, and x = 5/2 ± i(5√3/2).
(You can get them from x^3 + 125 = (x + 5)(x^2 − 5x + 25) and solving the quadratic.)
- Over the real numbers: 1 solution, x = −5.
- Over the complex numbers: 3 solutions (the three cube roots of −125),
x = −5, and x = 5/2 ± i(5√3/2).
(You can get them from x^3 + 125 = (x + 5)(x^2 − 5x + 25) and solving the quadratic.)
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