Question

Solve x^3-64=0, There are 3 solutions?

Answer 1

Do you know the formula to factor cubes?

Answer 2

(x-y)(x^2+xy+y^2)...?

Answer 3

a^3 + b^3 = (a + b)(a^2 – ab + b^2)
a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Answer 4

There could be 3 roots but it isnt always the case, to answer your question.

Answer 5

You would use the second one

so
(x-4)(x^2+4x+16)
right?

Answer 6

Yep. I got that. I also did x^3-64=0
x^3=64
and took the cube root of both so... x=4.
I guess I don't understand how to get the 3rd solution?

Answer 7

x=4 is one
and then to find the other 2
you have to use the quadratic formula

\[(-b \pm \sqrt{b ^{2}-4ac})\div2\]

Answer 8

Thanks!