document.write( "Question 426580: The sum of the squares of two numbers is 74 and the difference of their squares is 24. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #296728 by Alan3354(69443) $\"\"$ $\"About$

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Since the sum is even but not divisible by 4, the numbers are odd.
\n" ); document.write( "The sum is 74, so they're single digit numbers.
\n" ); document.write( "The difference is small, so they're consecutive odd numbers.
\n" ); document.write( "----------------------
\n" ); document.write( "24/4 = 6, the middle
\n" ); document.write( "--> 5 & 7
\n" ); document.write( "--------------
\n" ); document.write( "The hard way:
\n" ); document.write( " $\"x%5E2+%2B+y%5E2+=+74\"$
\n" ); document.write( " $\"x%5E2+-+y%5E2+=+24\"$
\n" ); document.write( "--------------------- Add
\n" ); document.write( " $\"2x%5E2+=+98\"$
\n" ); document.write( "x = 7
\n" ); document.write( "------
\n" ); document.write( "y = 5
\n" ); document.write( "Or -5 & -7 \n" ); document.write( "

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