Solving 4x3 + 4y =0 and 4y3 + 4x =0: Explained!

[rabihtawil]

Homework Statement

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

 

[Altabeh]

Homework Statement

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

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

AB

 

[rabihtawil]

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

AB

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

 

[vela]

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.

 

[rabihtawil]

First, fix your algebra mistake. You dropped a sign.

4x³ + 4y =0
x³ + y=0
y=-x³

NOW... plugging in

4y³ + 4x =0
y³ + x=0
(-x³)³ + x = 0

Once you fix that, you'll find you can factor the polynomial and solve for its roots.

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

 

[vela]

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

 

[rabihtawil]

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

-x⁹ + x = 0

now what?

 

[rabihtawil]

-x⁹ + x = 0

now what?

-x⁹ + x = 0
x(-x⁸ + 1) = 0

x = 0 or x= 1 right?

 

[vela]

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?

 

[rabihtawil]

Thank you so much, very appreciated!