document.write( "Question 219182: what is the only pair of consectutive integer whose square roots are also consecutive integer\r
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Algebra.Com's Answer #164890 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"n\"$ be the 1st integer
\n" ); document.write( "Then $\"n+%2B+1\"$ will be the 2nd integer
\n" ); document.write( "given:
\n" ); document.write( " $\"sqrt%28n%29+=+m\"$
\n" ); document.write( " $\"sqrt%28n%2B1%29+=+m%2B1\"$
\n" ); document.write( "Square both sides of both equations
\n" ); document.write( "(1) $\"n+=+m%5E2\"$
\n" ); document.write( " $\"n+%2B+1+=+%28m%2B1%29%5E2\"$
\n" ); document.write( "(2) $\"n+%2B+1+=+m%5E2+%2B+2m+%2B+1\"$
\n" ); document.write( "Substitute (1) in (2)
\n" ); document.write( " $\"m%5E2+%2B+1+=+m%5E2+%2B+2m+%2B+1\"$
\n" ); document.write( " $\"1+=+2m+%2B+1\"$
\n" ); document.write( " $\"2m+=+0\"$
\n" ); document.write( " $\"m+=+0\"$
\n" ); document.write( " $\"n+=+m%5E2\"$
\n" ); document.write( " $\"n+=+0\"$
\n" ); document.write( " $\"n%2B1+=+1\"$
\n" ); document.write( "The numbers are 0 and 1\r
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