document.write( "Question 73655: find two numbers whose sum is 12 and whose difference between their squares is 48.
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Algebra.Com's Answer #52676 by Earlsdon(6294) $\"\"$ $\"About$

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Let the two numbers be a and b. From the problem description, you can write:
\n" ); document.write( "1) $\"a%2Bb+=+12\"$ and
\n" ); document.write( "2) $\"a%5E2-b%5E2+=+48\"$
\n" ); document.write( "Rewrite equation 1) as: a = 12-b and substitute for the a in equation 2).
\n" ); document.write( "2a) $\"%2812-b%29%5E2-b%5E2+=+48\"$ Simplify and solve for b.
\n" ); document.write( " $\"%28144-24b%2Bb%5E2%29-b%5E2+=+48\"$
\n" ); document.write( " $\"144-24b+=+48\"$ Add 24b to both sides.
\n" ); document.write( " $\"144+=+48%2B24b\"$ Subtract 48 from both sides.
\n" ); document.write( " $\"96+=+24b\"$ Divide both sides by 24.
\n" ); document.write( " $\"4+=+b\"$ and...
\n" ); document.write( " $\"a+=+12-b\"$
\n" ); document.write( " $\"a+=+12-4\"$
\n" ); document.write( " $\"a+=+8\"$
\n" ); document.write( "The two numbers are 4 and 8
\n" ); document.write( "Check:
\n" ); document.write( " $\"a%2Bb+=+8%2B4\"$ = 12 Their sum is 12.
\n" ); document.write( " $\"a%5E2-b%5E2+=+8%5E2-4%5E2\"$
\n" ); document.write( " $\"64-16+=+48\"$ The difference of their squares is 48.\r
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