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 35996: 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 venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
.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?
> NO...SUPPOSE
a=2............AND
b=SQRT(3)....BOTH OF WHICH ARE DISTINCT REAL NUMBERS ,
THEN (a^2-b^2)=(a+b)(a-b)={2+SQRT(3)}{2-SQRT(3)}=2^2-{SQRT(3)}^2=4-3=1 IS A RATIONAL NUMBER WHERE AS A AND B ARE REAL NUMBERS ,BUT BE IS NOT A RATIONAL NUMBER.