document.write( "Question 189629: Find three consecutive integers such that the square of the sum of the smaller two is 144 more than the square of the largest. \n" ); document.write( "

Algebra.Com's Answer #142294 by josmiceli(19441) $\"\"$ $\"About$

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Call the consecutive integers
\n" ); document.write( " $\"a\"$ , $\"a%2B1\"$ , and $\"a%2B2\"$
\n" ); document.write( "The square of the sum of the smaller two is:
\n" ); document.write( " $\"%28a+%2B+a+%2B+1%29%5E2\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"%282a+%2B+1%29%5E2+=+%28a+%2B+2%29%5E2+%2B+144\"$
\n" ); document.write( " $\"4a%5E2+%2B+4a+%2B+1+=+a%5E2+%2B+4a+%2B+4+%2B+144\"$
\n" ); document.write( " $\"3a%5E2+%2B+4a+%2B+1+=+4a+%2B+148\"$
\n" ); document.write( " $\"3a%5E2+=+147\"$
\n" ); document.write( " $\"a%5E2+=+49\"$
\n" ); document.write( " $\"a+=+7\"$
\n" ); document.write( " $\"a%2B1+=+8\"$
\n" ); document.write( " $\"a+%2B+2+=+9\"$
\n" ); document.write( "The three consecutive integers are 7, 8, and 9
\n" ); document.write( "check:
\n" ); document.write( " $\"%28a+%2B+a+%2B+1%29%5E2+=+%28a+%2B+2%29%5E2+%2B+144\"$
\n" ); document.write( " $\"%287+%2B+8%29%5E2+=+9%5E2+%2B+144\"$
\n" ); document.write( " $\"225+=+81+%2B+144\"$
\n" ); document.write( " $\"225+=+225\"$
\n" ); document.write( "OK \n" ); document.write( "

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