document.write( "Question 695852: the product of two consecutive even numbers is 2208.what is the greatest number?
\n" ); document.write( "(note:i want short cut method) \n" ); document.write( "

Algebra.Com's Answer #428652 by mouk(232) $\"\"$ $\"About$

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Suppose the two consecutive even numbers are 2n and 2n+2\r
\n" ); document.write( "\n" ); document.write( " $\"+%282n%29%282n%2B2%29+=+2208+\"$
\n" ); document.write( " $\"+%282%29%28n%29%282%29%28n%2B1%29+=+2208+\"$
\n" ); document.write( " $\"+%284%29%28n%29%28n%2B1%29+=+2208+\"$
\n" ); document.write( " $\"+%28n%29%28n%2B1%29+=+552+\"$
\n" ); document.write( " $\"+n%5E2%2Bn+=+552+\"$
\n" ); document.write( " $\"+n%5E2%2Bn+-+552+=+0+\"$
\n" ); document.write( " $\"+%28n-23%29%28n%2B24%29+=+0+\"$
\n" ); document.write( "So $\"+n=23+\"$ or $\"+n=-24+\"$
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\n" ); document.write( "When n=23:
\n" ); document.write( "The two consecutive even numbers would be $\"+2n+\"$ and $\"+2n%2B2+\"$
\n" ); document.write( "ie 46 and 48 (whose product is 2208)\r
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\n" ); document.write( "When n=-24:
\n" ); document.write( "The two consecutive even numbers would be $\"+2n+\"$ and $\"+2n%2B2+\"$
\n" ); document.write( "ie -48 and -46 (whose product is 2208)
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\n" ); document.write( "So to answer the question, greatest number is 48 \n" ); document.write( "

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