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## Homework Statement

Show that the set S of all (x,y) ∈ ℝ

^{2}such that 2x

^{2+xy+y2}

is closed but not compact.

## Homework Equations

set S of all (x,y) ∈ ℝ

^{2}such that 2x

^{2+xy+y2}

## The Attempt at a Solution

I set x = 0 and then y = 0

giving me

[0,±√3] and [±√3,0] which means it is closed

However, for it to be Compact, it needs to be Closed & Bounded.

For it to be bounded, it must have both an upper and lower bound, which to me it appears to have?

The bound for me are when x and y = ±√3

Clearly I am wrong, given how the question is structured. Any ideas?