document.write( "Question 1075927: The sum of the squares of two consecutive even numbers is 84 more than the square of the next larger even number. What are the numbers? \n" ); document.write( "
Algebra.Com's Answer #690595 by ankor@dixie-net.com(22740)\"\" \"About 
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Let the two numbers be n and (n+2), the next larger even number is (n+4)
\n" ); document.write( "Write an equation for exactly what it says
\n" ); document.write( "\"the sum of the squares of two consecutive even numbers is 84 more than the square of the next larger even number.\"
\n" ); document.write( "n^2 + (n+2)^2 = (n+4)^2 + 84
\n" ); document.write( "FOIL
\n" ); document.write( "n^2 + n^2 + 4n + 4 = n^2 + 8n + 16 + 84
\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "n^2 + n^2 - n^2 + 4n - 8n + 4 - 16 - 84 = 0
\n" ); document.write( "n^2 - 4n - 96 = 0
\n" ); document.write( "we know these are integers so this will factor
\n" ); document.write( "(n-12)(n+8) = 0
\n" ); document.write( "The positive solution is what we want here
\n" ); document.write( "n = 12
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\n" ); document.write( "What are the numbers? 12 and 14
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\n" ); document.write( "Check this on your calc
\n" ); document.write( "12^2 + 14^2 =
\n" ); document.write( "16^2 + 84 =
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\n" ); document.write( ":
\n" ); document.write( "Note that the solution n = -8 will also satisfy the given requirement
\n" ); document.write( "-8^2 + -6^2 = -4^2 + 84
\n" ); document.write( "64 + 36 = 16 + 84 \n" ); document.write( "
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