document.write( "Question 79539: The product of two consecutive integers is 71 more than their sum. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #57074 by Earlsdon(6294) $\"\"$ $\"About$

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Let the two consecutive integers be x and (x+1). From the description you can write:
\n" ); document.write( " $\"x%2A%28x%2B1%29+=+x%2B%28x%2B1%29%2B71\"$ Simplify and solve for x.
\n" ); document.write( " $\"x%5E2%2Bx+=+2x%2B72\"$ Subtract 2x from both sides.
\n" ); document.write( " $\"x%5E2-x+=+72\"$ Subtract 72 from both sides.
\n" ); document.write( " $\"x%5E2-x-72+=+0\"$ Solve this quadratic equation by factoring.
\n" ); document.write( " $\"%28x-9%29%28x%2B8%29+=+0\"$ Apply the zero products principle.
\n" ); document.write( " $\"x-9+=+0\"$ or $\"x%2B8+=+0\"$ so...
\n" ); document.write( " $\"x+=+9\"$ or $\"x+=+-8\"$
\n" ); document.write( "So, there are really two answers to this problem and both would apply since the prolem did not limit the solution to positive integers.
\n" ); document.write( "1st. solution: x = 9 and x+1 = 10
\n" ); document.write( "2nd. solution: x = -8 and x+1 = -7\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "1st. solution:
\n" ); document.write( "9*10 = 90 and
\n" ); document.write( "9+10+71 = 90
\n" ); document.write( "2nd. solution:
\n" ); document.write( "-8*(-7) = 56 and
\n" ); document.write( "(-8)+(-7)+71 = -15+71 = 56\r
\n" ); document.write( "\n" ); document.write( "So you see, both solutions work and both sets of numbers are integers. \n" ); document.write( "

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