document.write( "Question 66105: If the sum of two consecutive integers is subtracted from their product, the result is 181. What are the two integers? \n" ); document.write( "

Algebra.Com's Answer #46836 by Earlsdon(6294) $\"\"$ $\"About$

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Let the first integer be n, the next consecutive integer is n+1.
\n" ); document.write( "From the problem description, you can write:
\n" ); document.write( " $\"n%28n%2B1%29+-+%28n+%2B+%28n%2B1%29%29+=+181\"$ Simplify and solve for n.
\n" ); document.write( " $\"n%5E2%2Bn-2n-1+=+181\"$
\n" ); document.write( " $\"n%5E2-n-182+=+0\"$ Solve this quadratic equation by factoring:
\n" ); document.write( " $\"%28n%2B13%29%28n-14%29+=+0\"$ Apply the zero product principle:
\n" ); document.write( " $\"n%2B13+=+0\"$ and/or $\"n-14+=+0\"$
\n" ); document.write( "If $\"n%2B13+=+0\"$ then $\"n+=+-13\"$ and $\"n%2B1+=+-12\"$
\n" ); document.write( "If $\"n-14+=+0\"$ then $\"n+=+14\"$ and n+1 = 15\r
\n" ); document.write( "\n" ); document.write( "So you really get two pairs of integers which satisfy the given constraints and since the problem did not restrict the solution to positive integers only, you will have two answers:\r
\n" ); document.write( "\n" ); document.write( "14 and 15 is one pair.
\n" ); document.write( "-13 and -12 is the other pair.\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " $\"%2814%29%2815%29-%2814%2B15%29+=+210+-+29\"$ = $\"181\"$ OK
\n" ); document.write( " $\"%28-13%29%28-12%29+-+%28-13+%2B+%28-12%29%29+=+156+-+%28-25%29\"$ = $\"156+%2B+25+=+181\"$ OK \n" ); document.write( "

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