# Homework Help: How to derive inequalities

1. May 28, 2009

### thrill3rnit3

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

Derive the following inequality.

2. Relevant equations

x$$^{2}$$+xy+y$$^{2}$$ $$\geq$$ 0

3. The attempt at a solution

I don't know how to get started. How do you derive inequalities?

I'm not looking for the answer, just general tips.

Last edited: May 28, 2009
2. May 28, 2009

### danago

That term on the left looks similar to (x+y)(x+y). How could you use that?

3. May 28, 2009

### thrill3rnit3

(x+y) squared has +2xy as its middle term

4. May 29, 2009

### Staff: Mentor

I don't think the similarity (or not) to (x + y)(x + y) is any help.

Think about the equation x2 + xy + y2 = 0.
Are there any real solutions to this equation?

If yes, then the real solutions (x, y) are the graph of a curve that separates the portion of the plane for which x2 + xy + y2 > 0 from the other portion of the plane where x2 + xy + y2 < 0.

If no, then all points (x, y) in the plane must satisfy exactly one of the inequalities listed in the previous paragraph.