document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #22048 by venugopalramana(3286) $\"\"$ $\"About$

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.If a and b are distinct real numbers such that a-b and a^2-b^2 are
\n" ); document.write( "> rational, must a and b be rational?
\n" ); document.write( "> NO...SUPPOSE
\n" ); document.write( "a=2............AND
\n" ); document.write( "b=SQRT(3)....BOTH OF WHICH ARE DISTINCT REAL NUMBERS ,
\n" ); document.write( "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. \n" ); document.write( "

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