# Homework Help: Solve equation

1. Jan 23, 2010

### rabihtawil

1. The problem statement, all variables and given/known data

how to solve this:

4x3 + 4y =0
4y3 + 4x =0

the solution is x = 0,1,-1
y = 0,-1,1

how did they bring such result

2. Jan 23, 2010

### Altabeh

Find y from the first equation and then plug it into the second one so you're done!

AB

3. Jan 23, 2010

### rabihtawil

4x3 + 4y =0
x3 + y=0
y=x3

NOW........... plugging in

4y3 + 4x =0
y3 + x=0
(x3)3 + x = 0

now what?? how do i continue from here :S

4. Jan 23, 2010

### vela

Staff Emeritus
First, fix your algebra mistake. You dropped a sign. Once you fix that, you'll find you can factor the polynomial and solve for its roots.

5. Jan 23, 2010

### rabihtawil

4x3 + 4y =0
x3 + y=0
y=-x3

NOW........... plugging in

4y3 + 4x =0
y3 + x=0
(-x3)3 + x = 0

Please i am stuck show me how, i know it should be factored by x but how?

Last edited: Jan 23, 2010
6. Jan 23, 2010

### vela

Staff Emeritus
First, simplify (-x3)3. What do you get?

7. Jan 23, 2010

### rabihtawil

-x9 + x = 0

now what?

8. Jan 23, 2010

### rabihtawil

-x9 + x = 0
x(-x8 + 1) = 0

x = 0 or x= 1 right?

9. Jan 23, 2010

### vela

Staff Emeritus
You can flip the sign of the whole equation to make it a little simpler to work with:

x9-x=0

Now you have a common factor of x in both terms, so factor it out.

OK, you posted while I was writing. :) So you have

x(x8-1) = 0

So this means x=0 or x8-1=0, right? So you have one of the roots so far.

Note that x8-1=(x4)2-12 is a difference of squares, so what does it factor into?

10. Jan 23, 2010

### rabihtawil

Thank you so much, very appreciated!