document.write( "Question 162007: find three consecutive integers such that the sum of the squares of the second and the third exceeds the square of the first by 21. \n" ); document.write( "

Algebra.Com's Answer #119396 by josmiceli(19441) $\"\"$ $\"About$

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Call the cosecutive integers $\"n\"$ , $\"n%2B1\"$ , $\"n%2B2\"$
\n" ); document.write( "Given:
\n" ); document.write( " $\"%28n%2B1%29%5E2+%2B+%28n%2B2%29%5E2+=+n%5E2+%2B+21\"$
\n" ); document.write( " $\"n%5E2%2B+2n+%2B+1+%2B+n%5E2+%2B+4n+%2B+4+=+n%5E2+%2B+21\"$
\n" ); document.write( " $\"2n%5E2+%2B+6n+%2B+5+=+n%5E2+%2B+21\"$
\n" ); document.write( " $\"n%5E2+%2B+6n+-+16+=+0\"$
\n" ); document.write( " $\"%28n+%2B+8%29%28n+-+2%29+=+0\"$
\n" ); document.write( "Either
\n" ); document.write( " $\"n+%2B+8+=+0\"$
\n" ); document.write( " $\"n+=+-8\"$
\n" ); document.write( "or
\n" ); document.write( " $\"n+-+2+=+0\"$
\n" ); document.write( " $\"n+=+2\"$
\n" ); document.write( "Use the positive result
\n" ); document.write( " $\"n%2B1+=+3\"$
\n" ); document.write( " $\"n%2B2+=+4\"$
\n" ); document.write( "The numbers are 2,3,and 4
\n" ); document.write( "check answer:
\n" ); document.write( " $\"%28n%2B1%29%5E2+%2B+%28n%2B2%29%5E2+=+n%5E2+%2B+21\"$
\n" ); document.write( " $\"3%5E2+%2B+4%5E2+=+2%5E2+%2B+21\"$
\n" ); document.write( " $\"9+%2B+16+=+4+%2B+21\"$
\n" ); document.write( " $\"25+=+25\"$
\n" ); document.write( "OK \n" ); document.write( "

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