Is the Equation x^4 + y^4 - xy^2 = x^2y Solvable or Simplifiable?

[kyphysics]

Homework Statement

x^4 + y^4 - xy^2 = x^2y

Homework Equations

None. However, I'm using "^" to represent an exponent operation.

The Attempt at a Solution

Not sure. That's why I'm asking. It just feels to me that everything is an unlike term and thus you can't do anything.

Is that correct here? Thanks for the help everyone!

 

[haruspex]

How do you mean 'solved'? Do you mean finding roots?
Is this the whole question as given to you? If not, please post the original question.

 

[statdad]

You can do a little factoring by subtracting a convenient amount from each side, but without knowing what your goal is I'm not sure what benefit would result.

 

[berkeman]

Homework Statement

x^4 + y^4 - xy^2 = x^2y

Homework Equations

None. However, I'm using "^" to represent an exponent operation.

The Attempt at a Solution

Not sure. That's why I'm asking. It just feels to me that everything is an unlike term and thus you can't do anything.

Is that correct here? Thanks for the help everyone!

If I understand what you wrote, it looks like x=y=1 is a solution by inspection. Where is the equation from?

 

[Mark44]

If I understand what you wrote, it looks like x=y=1 is a solution by inspection.

As are x = 0, y = 0.

 

[LCKurtz]

Here's a graph, for what it's worth. I've included $y=\pm x$ in the picture:

Click on it for a better view.

 

[berkeman]

Very Cool :-)

 

[kyphysics]

How do you mean 'solved'? Do you mean finding roots?
Is this the whole question as given to you? If not, please post the original question.

First, Merry Christmas! lol.

I just logged back in here after getting bored today and wanting to catch up on my threads! Sorry it's taken so long, but thanks for the answers!

As for the "original question," this is what was written on the board of our class by some girl doing some stuff after class. It's not from any worksheet I had from the class (I even doubled-chcked), but was just a random "problem" I saw on the board and was puzzled by when I glanced at it and thought I'd jot it down.

My question is whether anything can be done arithmetic-wise to combine what seem like unlike terms? And also, can the equation be solved above in any way?