document.write( "Question 214333: Does anyone know how to go about this problem? The difference of two positive numbers is 3 and the sum of their squares is 65. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #161891 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
let the numbers be $\"j\"$ and $\"k\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"k+-+j+=+3\"$
\n" ); document.write( "(2) $\"j%5E2+%2B+k%5E2+=+65\"$
\n" ); document.write( "From (1),
\n" ); document.write( " $\"k+=+j+%2B+3\"$
\n" ); document.write( " $\"j%5E2+%2B+%28j+%2B+3%29%5E2+=+65\"$
\n" ); document.write( " $\"j%5E2+%2B+j%5E2+%2B+6j+%2B+9+=+65\"$
\n" ); document.write( " $\"2j%5E2+%2B+6j+-+56+=+0\"$
\n" ); document.write( " $\"j%5E2+%2B+3j+-+28+=+0\"$
\n" ); document.write( "solve using quadratic equation
\n" ); document.write( " $\"j+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+3\"$
\n" ); document.write( " $\"c+=+-28\"$
\n" ); document.write( " $\"j+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-28%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"j+=+%28-3+%2B-+sqrt%28+9+%2B+112+%29%29%2F2+\"$
\n" ); document.write( " $\"j+=+%28-3+%2B-+sqrt%28+121+%29%29%2F2+\"$
\n" ); document.write( " $\"j+=+%28-3+%2B+11%29%2F2\"$
\n" ); document.write( " $\"j+=+4\"$
\n" ); document.write( "and
\n" ); document.write( " $\"j+=+%28-3+-+11%29%2F2\"$
\n" ); document.write( " $\"j+=+-7\"$ (can't use negative result)
\n" ); document.write( " $\"k+=+j+%2B+3\"$
\n" ); document.write( " $\"k+=+7\"$
\n" ); document.write( "The numbers are 4 and 7
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"j%5E2+%2B+k%5E2+=+65\"$
\n" ); document.write( " $\"4%5E2+%2B+7%5E2+=+65\"$
\n" ); document.write( " $\"16+%2B+49+=+65\"$
\n" ); document.write( " $\"65+=+65\"$ OK\r
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