document.write( "Question 1118978: Find two numbers such that the smaller subtracted from the larger is 9 and the difference of the square of the larger subtracted from square of the smaller is 9. \n" ); document.write( "

Algebra.Com's Answer #734403 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( "Let a be the larger number and b the smaller. Then

\n" ); document.write( "(1) $\"a-b+=+9\"$
\n" ); document.write( "(2) $\"a%5E2-b%5E2+=+9\"$

\n" ); document.write( "Dividing (2) by (1) gives

\n" ); document.write( "(3) $\"a%2Bb+=+1\"$

\n" ); document.write( "Then (1) and (2) with a little algebra give the answer:

\n" ); document.write( "a = 5; b = -4

\n" ); document.write( "If you are good with mental arithmetic, you might realize that the only time the squares of two integers differ by 9 is with $\"5%5E2-4%5E2+=+9\"$ . So the absolute values of the two numbers are 5 and 4; then to get a difference of 9 between the two numbers, you get the answers 5 and -4.

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\n" ); document.write( "Tutor @ikleyn is right; I didn't read the question carefully enough.

\n" ); document.write( "Since it is the smaller subtracted from the larger that gives a result of 9, the numbers are 4 and -5; not 5 and -4. \n" ); document.write( "

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