document.write( "Question 148437: the sum of the squares of two consecutive even integers is 52. what are the integers? I believe the answers is 4^2 and 6^2 but I can't figure out how to write an equation to show how I figured it out, Please help!!! \n" ); document.write( "

Algebra.Com's Answer #108785 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Try this!
\n" ); document.write( "Let x be the first even integer, then (x+2) is the next consecutive even integer.
\n" ); document.write( "The sum of their squares is expressed by:
\n" ); document.write( " $\"x%5E2%2B%28x%2B2%29%5E2\"$ and this is equal to 52, so you can write the equation:
\n" ); document.write( " $\"x%5E2%2B%28x%2B2%29%5E2+=+52\"$ Simply this.
\n" ); document.write( " $\"x%5E2%2B%28x%5E2%2B4x%2B4%29+=+52\"$ Combine like-terms and subtract 52 from both sides.
\n" ); document.write( " $\"2x%5E2%2B4x-48+=+0\"$ Now you have a quadratic equation that can be solved by factoring after dividing through by 2 to simplify it a bit.
\n" ); document.write( " $\"x%5E2%2B2x-24+=+0\"$ Factor.
\n" ); document.write( " $\"%28x-4%29%28x%2B6%29+=+0\"$ from which you get:
\n" ); document.write( " $\"x+=+4\"$ or $\"x+=+-6\"$
\n" ); document.write( "The integers are 4 and 6 or -6 and -4
\n" ); document.write( "Check:
\n" ); document.write( " $\"4%5E2%2B6%5E2=+16%2B36\"$ = $\"52\"$ or...
\n" ); document.write( " $\"%28-6%29%5E2%2B%28-4%29%5E2+=+36%2B16\"$ = $\"52\"$ \r
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