SOLUTION: If a and b are distinct real numbers such that a-b and a^2 -b^2 are rational, must a and b be rational?

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Question 35939: If a and b are distinct real numbers such that a-b and a^2 -b^2 are rational, must a and b be rational?
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
Yes both a and b must be rational. The reason for this is that given a-b and a%5E2+-+b%5E2 you can calculate both a and b using only addition, subtraction, and division. There is no way to make irrational numbers from rational ones using only these operators.
To start you off in trying to find a and b, Ask yourself, what is %28a%5E2-b%5E2%29%2F%28a-b%29
Hope that helps,
Write back if you need me to do all the stages, but do try and find a and b on your own first.
Kev