document.write( "Question 248681: Product of two consecutive integers is 89 more than their sum. Find integers \n" ); document.write( "
Algebra.Com's Answer #181208 by richwmiller(17219)\"\" \"About 
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We know they are integers.
\n" ); document.write( "Let a and a+1 be the integers
\n" ); document.write( "a(a+1)=89+a+a+1
\n" ); document.write( "a^2+a=89+2a+1
\n" ); document.write( "a^2+a=90+2a
\n" ); document.write( "a^2-a=90
\n" ); document.write( "a^2-a-90=0
\n" ); document.write( "factor 90 that have a difference of 1
\n" ); document.write( "(9,10) done
\n" ); document.write( "(a+9)(a-10)=0
\n" ); document.write( "a=-9 (-9, -8)
\n" ); document.write( "and a=10 (10,11)
\n" ); document.write( "integers can be positive or negative
\n" ); document.write( "so we have two sets of possibilities.
\n" ); document.write( "we need to check them with the equation
\n" ); document.write( "a(a+1)=89+a+(a+1)
\n" ); document.write( "(-9)*(-8)=89+(-9)+(-8)
\n" ); document.write( "72=89-17
\n" ); document.write( "72=72
\n" ); document.write( "yes
\n" ); document.write( "let's try the positive numbers
\n" ); document.write( "10*11=89+10+11
\n" ); document.write( "110=110
\n" ); document.write( "yes
\n" ); document.write( "So we have two sets of integers
\n" ); document.write( "(-9,-8) and (9,10) \n" ); document.write( "
\n" );