document.write( "Question 567957: find the triple of consecutive integers such that 11 times the largest of the integers is 46 more than the product of the other two \n" ); document.write( "
Algebra.Com's Answer #366822 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Call the integers \"+n+\", \"+n%2B1+\", and \"+n%2B2+\"
\n" ); document.write( "given:
\n" ); document.write( "\"+11%2A%28+n%2B2+%29+=+n%2A%28+n%2B1+%29+%2B+46+\"
\n" ); document.write( "\"+11n+%2B+22+=+n%5E2+%2B+n+%2B+46+\"
\n" ); document.write( "\"+n%5E2+-+10n+%2B+24+=+0+\"
\n" ); document.write( "complete the square:
\n" ); document.write( "\"+n%5E2+-+10n+%2B+%28-10%2F2%29%5E2+=+-24+%2B+%28-10%2F2%29%5E2+\"
\n" ); document.write( "\"+%28+n+-+5+%29%5E2+=+-24+%2B+25+\"
\n" ); document.write( "\"+n+-+5+=+1+\"
\n" ); document.write( "\"+n+=+6+\"
\n" ); document.write( "also,
\n" ); document.write( "\"+n+-+5+=+-1+\"
\n" ); document.write( "\"+n+=+4+\"
\n" ); document.write( "------------
\n" ); document.write( "If the numbers are:
\n" ); document.write( "\"+n+=+6+\"
\n" ); document.write( "\"+n+%2B1+=+7+\"
\n" ); document.write( "\"+n+%2B+2+=+8+\"
\n" ); document.write( "\"+11%2A%28+n%2B2+%29+=+n%2A%28+n%2B1+%29+%2B+46+\"
\n" ); document.write( "\"+11%2A8+=+6%2A7+%2B+46+\"
\n" ); document.write( "\"+88+=+42+%2B+46+\"
\n" ); document.write( "\"+88+=+88+\"
\n" ); document.write( "OK
\n" ); document.write( "If the numbers are:
\n" ); document.write( "\"+n+=+4+\"
\n" ); document.write( "\"+n+%2B+1+=+5+\"
\n" ); document.write( "\"+n+%2B+2+=+6+\"
\n" ); document.write( "\"+11%2A%28+n%2B2+%29+=+n%2A%28+n%2B1+%29+%2B+46+\"
\n" ); document.write( "\"+11%2A6+=+4%2A5+%2B+46+\"
\n" ); document.write( "\"+66+=+20+%2B+46+\"
\n" ); document.write( "\"+66+=+66+\"
\n" ); document.write( "OK
\n" ); document.write( "The consecutive integers can be:
\n" ); document.write( "6,7, and 8
\n" ); document.write( "or
\n" ); document.write( "4,5, and 6 \n" ); document.write( "
\n" );