document.write( "Question 865115: find three consecutive odd integers such that the sum of all three is 42 less than the product of the larger two \n" ); document.write( "

Algebra.Com's Answer #521559 by KMST(5328) $\"\"$ $\"About$

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Let's call those numbers $\"n-2\"$ , $\"n\"$ , and $\"n%2B2\"$ .
\n" ); document.write( "(Those are 3 numbers, with each greater than the one before by 2.
\n" ); document.write( "The approach could be the same for a problem involving 3 consecutive even numbers.
\n" ); document.write( "For this problem, when we solve for $\"n\"$ , $\"n\"$ needs to be an odd number.
\n" ); document.write( "If we found a value for

is the sum of all three consecutive odd integers.
\n" ); document.write( " $\"n%28n%2B2%29\"$ is the product of the larger two consecutive odd integers.
\n" ); document.write( "The problem states that
\n" ); document.write( " $\"%28n-2%29%2Bn%2B%28n%2B2%29=n%28n%2B2%29-42\"$ or $\"3n=n%28n%2B2%29-42\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"3n=n%28n%2B2%29-42\"$ --> $\"3n=n%5E2%2B2n-42\"$ --> $\"n%5E2%2B2n-42-3n=0\"$ --> $\"n%5E2-n-42=0\"$
\n" ); document.write( "That last equation is easy to solve by factoring:
\n" ); document.write( " $\"n%5E2-n-42=0\"$ --> $\"%28n%2B6%29%28n-7%29=0\"$ --> $\"system%28either%2Cn%2B6=0%2Cor%2Cn-7=0%29\"$ --> $\"system%28either%2Cn=-6%2Cor%2Cn=7%29\"$ .
\n" ); document.write( "Since we are expecting $\"n\"$ to be an odd integer, $\"highlight%28n=7%29\"$ ,
\n" ); document.write( "and the three consecutive odd integers are
\n" ); document.write( " $\"n-2=7-2=highlight%285%29\"$ , $\"n=highlight%287%29\"$ , and $\"n%2B2=7%2B2=highlight%289%29\"$ .
\n" ); document.write( " \n" ); document.write( "

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