document.write( "Question 222965: what is the product of two consecutive integers is 1 more than their sum. Find the integers? \n" ); document.write( "
Algebra.Com's Answer #166817 by jsmallt9(3758)\"\" \"About 
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Consecutive integers are 1 apart from each other. So if one integer is \"x\" then the next one is \"x+1\". Now let's use these to translate
\n" ); document.write( "\"the product of two consecutive integers is 1 more than their sum\"

\n" ); document.write( "Product means multiplication so \"the product of two consecutive integers\" is (x)(x+1). Sum means addition so \"their sum\" is (x) + (x+1)

\n" ); document.write( "So \"the product of two consecutive integers is 1 more than their sum\" translates into:
\n" ); document.write( "\"%28x%29%28x%2B1%29+=+1+%2B+%28x%29+%2B+%28x%2B1%29\"
\n" ); document.write( "Now we just need to solve this. Start by simplifying each side:
\n" ); document.write( "\"x%5E2+%2B+x+=+2x+%2B+2\"
\n" ); document.write( "Next, since this is a quadratic equation (because of the \"x%5E2\"), we will get one side equal to zero by subtracting the entire right side from both sides:
\n" ); document.write( "\"x%5E2+-+x+-+2+=+0\"
\n" ); document.write( "Now we can solve this by factoring (or by using the quadratic formula):
\n" ); document.write( "\"x+-+2%29%28x+%2B+1%29+=+0\"
\n" ); document.write( "The Zero Product Property tells us that if this or any product is equal to zero then one or more of the factors must be zero. So:
\n" ); document.write( "\"x-2+=+0\" or \"x%2B1+=+0\"
\n" ); document.write( "Solving each of these simple equations we get:
\n" ); document.write( "\"x+=+2\" or \"x+=+-1\"
\n" ); document.write( "Now remember what \"x\" represents. (Look back at the beginning.) It represents the first (or smaller) of the two consecutive integers. And (x+1) represents the second (or larger) of the two. We have found two values for x: 2 and -1. So we have found two pairs of consecutive integers:
  • 2 and 3
  • -1 amd 0

\n" ); document.write( "You can check them out and they both work:
  • 2*3 is one more than 2+3
  • -1*0 is one more than -1+0
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