document.write( "Question 282198: Find 3 consecutive even numbers where the product of the smaller two numbers is 40 less than the square of the largest number. \n" ); document.write( "

Algebra.Com's Answer #204903 by oberobic(2304) $\"\"$ $\"About$

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Three consecutive numbers could be called: a, b, c.
\n" ); document.write( "But it is far better to define them as:
\n" ); document.write( " $\"a+=+x\"$
\n" ); document.write( " $\"b+=+x%2B1\"$
\n" ); document.write( " $\"c+=+x%2B2\"$
\n" ); document.write( ".
\n" ); document.write( " $\"a%2Ab+=+c%5E2+-40\"$ :: the product of the two smaller is 40 less than the square of the largest
\n" ); document.write( ".
\n" ); document.write( " $\"x%28x%2B1%29+=+%28x%2B2%29%5E2+-40\"$
\n" ); document.write( " $\"x%5E2%2Bx+=+x%5E2%2B4x%2B4+-40\"$
\n" ); document.write( " $\"x%5E2%2Bx+-x%5E2+-4x+=+-36\"$
\n" ); document.write( " $\"-3x+=+-36\"$
\n" ); document.write( " $\"x+=+12\"$
\n" ); document.write( " $\"x+%2B+1+=+13\"$
\n" ); document.write( " $\"x+%2B+2+=14\"$
\n" ); document.write( ".
\n" ); document.write( "Checking...
\n" ); document.write( " $\"12%2A13+=+156\"$
\n" ); document.write( " $\"14%2A14+=+196\"$
\n" ); document.write( "So
\n" ); document.write( " $\"12%2A13+=+14%5E2+-+40\"$
\n" ); document.write( "Correct.
\n" ); document.write( ".
\n" ); document.write( "Answer:
\n" ); document.write( "The three consecutive numbers are: 12, 13, and 14.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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