Question

solve x^3=-1
am I right -1

Answer 1

@Directrix

Answer 2

This is a polynomial (called a cubic) so I'm expecting 3 roots.
x^3=-1

Let's see.

Answer 3

try factoring
x^3+1 as a first step

Answer 4

x=-1?

Answer 5

@cutegirl x = -1 is one of the three answers. So, there's more work to do.

Answer 6

ow i c..

Answer 7

@cutegirl I just had a thought. In the instructions, were you told to find the real number values of x or to solve for x over the set of complex numbers? The complex numbers are the union of the set of reals and the set of imaginaries.

Answer 8

no this was all

Answer 9

Well I'm curious on how this is done...

Answer 10

@cutegirl girl have you ever seen how to factor a sum of cubes?

Answer 11

yea...

Answer 12

the reason I'm saying this is because you have x^3=-1
and if you add 1 on both sides you have x^3+1=0

Answer 13

the first step is to factor the left hand side

Answer 14

then set each factor equal to 0
since a*b=0 implies a=0 or b=0 or both =0

Answer 15

yea but zero is not a choice for me..

Answer 16

I didn't say 0 was an answer

Answer 17

so (x + 1)(x^2 - x + 1) = 0

Answer 18

beautiful

Answer 19

now set each factor =0

Answer 20

x+1=0 or x^2-x+1=0

Answer 21

and solve

Answer 22

x + 1) = 0 or (x^2 - x + 1) = 0

Answer 23

yep then solve the x+1=0 equation
and solve the x^2-x+1=0

Answer 24

x=-1

Answer 25

the first equation I'm asking you to solve you actually already solved and got x=-1
x+1=0 implies x=-1 beause if you subtract 1 on both sides you get x+1-1=0-1
=> x+0=-1 => x=-1

but the x^2-x+1=0 is a little more difficult to solve
you need the quadratic formula
or completing the square

Answer 26

-1^2/3

Answer 27

hmmm...
have you ever solved a quadratic equation before?

Answer 28

im not good at them

Answer 29

\[ax^2+bx+c=0 , a \neq 0 \\ \text{ \implies } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \]

Answer 30

you need to identify a,b, and c from x^2-x+1=0

Answer 31

you write that same equation as 1x^2-1x+1=0

Answer 32

a=?
b=?
c=?

Answer 33

this is the answer x = -1, x = ( 1 +- i (sqr(3)) / 2

Answer 34

lol
yeah