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## Homework Statement

Prove that if x is a real number then 2x

^{2}-3=0

## Homework Equations

## The Attempt at a Solution

Well I think this proof is OK but it seems very to the point, please tell me if there is any fallacy in my reasoning.

2x

^{2}-3=0

2x

^{2}=3

but 2x

^{2}is even, while 3 is odd

Hence x must be irrational for all real x.

??