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## Homework Statement

Prove that for all x ∈ ℝ, at least one of √3 - x and √3 +x is irrational.

## Homework Equations

## The Attempt at a Solution

I understand how to prove that √3 is a irrational number by proof by contradiction. However I am not sure how to prove this one.

Would I have to equate √3 - x = a/b and √3 + x = a/b and prove by contradiction?

Thank you.