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

Algebra.Com's Answer #22087 by kev82(151) $\"\"$ $\"About$

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Hi,\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "To start you off in trying to find a and b, Ask yourself, what is $\"%28a%5E2-b%5E2%29%2F%28a-b%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Hope that helps,\r
\n" ); document.write( "\n" ); document.write( "Write back if you need me to do all the stages, but do try and find a and b on your own first.\r
\n" ); document.write( "\n" ); document.write( "Kev \n" ); document.write( "

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