Can This be Simplified or Solved?

  • Thread starter kyphysics
  • Start date
In summary, the conversation is about a student's attempt to solve an equation and asking for help. The equation given is x^4 + y^4 - xy^2 = x^2y and the student is unsure if anything can be done to simplify it. They also ask if it can be solved and provide a graph and solutions by inspection.
  • #1
kyphysics
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436

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!
 
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  • #2
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.
 
  • #3
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.
 
  • #4
kyphysics said:

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?
 
  • #5
berkeman said:
If I understand what you wrote, it looks like x=y=1 is a solution by inspection.
As are x = 0, y = 0.
 
  • #6
Here's a graph, for what it's worth. I've included ##y=\pm x## in the picture:
graph.jpg

Click on it for a better view.
 
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Likes berkeman
  • #7
Very Cool :-)
 
  • #8
haruspex said:
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?
 

1. What is the process for simplifying or solving a problem?

The process for simplifying or solving a problem involves breaking the problem down into smaller, more manageable parts, identifying any underlying patterns or relationships, and using logical reasoning and problem-solving techniques to find a solution.

2. How do I know when a problem can be simplified or solved?

A problem can usually be simplified or solved if it is well-defined and has a clear objective or goal. It is also important to consider if there is enough information available to solve the problem and if the problem is within your level of expertise.

3. What are some common techniques for simplifying or solving a problem?

Some common techniques for simplifying or solving a problem include brainstorming, breaking the problem into smaller parts, using visual aids such as diagrams or charts, and seeking input or advice from others.

4. How do I know if I have found the most efficient solution to a problem?

Finding the most efficient solution to a problem involves evaluating the effectiveness, practicality, and complexity of the solution. It is also important to consider if the solution addresses all aspects of the problem and if it can be easily implemented.

5. What should I do if I am struggling to simplify or solve a problem?

If you are struggling to simplify or solve a problem, try approaching it from a different perspective or seek input from others. You can also take a break and come back to the problem with a fresh mind. If the problem is complex, it may be helpful to break it down into smaller, more manageable parts.

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