document.write( "Question 586422: there are three consecutive integers. the product of the first two plus the third integer is equal to 101 \n" ); document.write( "

Algebra.Com's Answer #373890 by KMST(5328) $\"\"$ $\"About$

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Let the integers be n, n+1, and n+2.
\n" ); document.write( "The product of the first two is $\"n%28n%2B1%29=n%5E2%2Bn\"$
\n" ); document.write( "That plus the third integer is $\"n%5E2%2Bn%2Bn%2B2=n%5E2%2B2n%2B2\"$
\n" ); document.write( "If $\"n%5E2%2B2n%2B2=101\"$ --> $\"n%5E2%2B2n=99\"$ (subtracting 2 from both sides).
\n" ); document.write( "Now we can complete the square to solve the quadratic equation:
\n" ); document.write( " $\"n%5E2%2B2n=99\"$ --> $\"n%5E2%2B2n%2B1=99%2B1\"$ --> $\"%28n%2B1%29%5E2=100\"$ --> $\"n%2B1=10\"$
\n" ); document.write( "The integers are 9, 10, and 11.
\n" ); document.write( " $\"9%2A10%2B11=90%2B11=101\"$
\n" ); document.write( "NOTE: There are other ways to solve that quadratic equation (factoring, the quadratic formula), but completing the square looked easier. \n" ); document.write( "

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