document.write( "Question 1140662: The product of two consecutive integers is 36 less than six times their sum. Find the integers. Given the answers as comma-separated numbers in ascending order.
\n" ); document.write( "I only can find one set of numbers every time never two. If I do find the two, I do find the two and I'm off by a negative or I did the next number down besides up.
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Algebra.Com's Answer #761188 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "n*(n+1) = 6*(n+(n+1)) - 36\r\n" );
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document.write( "n^2 + n = 12n + 6 - 36\r\n" );
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document.write( "n^2 - 11n + 30 = 0\r\n" );
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document.write( "(n-5)*(n-6) = 0\r\n" );
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document.write( "There are two roots:  n= 5  and  n= 6.\r\n" );
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document.write( "CHECK for n= 5:  5*(5+1) = 5*6 = 30;   6*(5+6) - 36 = 6*11 - 36 = 66 - 36 = 30, the same number.   ! Correct !\r\n" );
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document.write( "CHECK for n= 6:  6*(6+1) = 6*7 = 42;   6*(6+7) - 36 = 6*13 - 36 = 78 - 36 = 42, the same number.   ! Correct !\r\n" );
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document.write( "ANSWER.  The problem has TWO PAIRS of consecutive integer solutions:  (5,6)  and  (6,7).\r\n" );
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