Question

Does x^3=8 Have two solutions as x^2=4 does? why or why not

Answer 1

If you're considering real numbers only (and not complex/imaginary ones), then x^3 = 8 has only one solution and it is x = 2. We don't have the plus minus going on here. This is because (-2)^3 = -8 and not 8. We have three copies of -2 multiplied out to make a negative result.

If you consider complex/imaginary solutions, then x^3 = 8 has three solutions. The other two solutions are
`-1+i√(3)` and
`-1-i√(3)` where
`i = √(-1)`. If your teacher hasn't covered this chapter yet, then ignore this paragraph.