document.write( "Question 32202: If c is asn odd integer, the show that the equation x^2+x-c=0 has no integer solutions. \n" ); document.write( "

Algebra.Com's Answer #18734 by Fermat(136) $\"\"$ $\"About$

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x² + x - c = 0
\n" ); document.write( "using the quadratic formula,
\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+1%2B4c+%29%29%2F2+\"$
\n" ); document.write( "Let D = 1 + 4c
\n" ); document.write( "For integer solutions for x, we require $\"sqrt%28D%29\"$ must be odd.
\n" ); document.write( ".: D = odd*odd = odd
\n" ); document.write( ".: 1 + 4c = odd
\n" ); document.write( "4c = even
\n" ); document.write( "=> c = even
\n" ); document.write( "=========== \n" ); document.write( "

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