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?
>  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.