Question

x^3 = 125 , 3 solutions?

Answer 1

X can be 5.

Answer 2

$$\huge x^3 = x•x•x$$

Answer 3

There is three solutions (two are imaginary). You'd have to first write 125 in trigonometric form: \(\large 125 (\cos 0 + i \sin 0)\) and then you can use the method for finding roots of a complex number.

Alternatively, \[\large x^3 = 125\]\[\large x^3 -5^3 = 0\]difference of two cubes\[\large (x -5)(x^2+5x +25)= 0\]then factor that quadratic to find the resulting two solutions.

An equation of the form \(\large x^n = c\) always has \(\large n\) solutions, but most are imaginary.

Answer 4

*use the quadratic formula, since you can't factor it.