document.write( "Question 165236: 36.) Show a complete solution to the problem.\r
\n" ); document.write( "\n" ); document.write( "Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #121793 by josmiceli(19441) $\"\"$ $\"About$

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Call the numbers $\"a\"$ and $\"b\"$
\n" ); document.write( "(1) $\"b+-+a+=+11\"$
\n" ); document.write( "(2) $\"sqrt%28b%29+-+sqrt%28a%29+=+1\"$
\n" ); document.write( "Let $\"c%5E2+=+a\"$
\n" ); document.write( "Let $\"d%5E2+=+b\"$
\n" ); document.write( "------------------
\n" ); document.write( " $\"d%5E2+-+c%5E2+=+11\"$
\n" ); document.write( " $\"%28d+-+c%29%28d+%2B+c%29+=+11\"$
\n" ); document.write( " $\"d+-+c+=+1\"$
\n" ); document.write( " $\"1%2A%28d+%2B+c%29+=+11\"$
\n" ); document.write( " $\"d+%2B+c+=+11\"$
\n" ); document.write( "Add these equations
\n" ); document.write( " $\"2d+=+12\"$
\n" ); document.write( " $\"d+=+6\"$
\n" ); document.write( " $\"d+-+c+=+1\"$
\n" ); document.write( " $\"6+-+c+=+1\"$
\n" ); document.write( " $\"c+=+5\"$
\n" ); document.write( "--------------
\n" ); document.write( " $\"c%5E2+=+a\"$
\n" ); document.write( " $\"5%5E2+=+a\"$
\n" ); document.write( " $\"a+=+25\"$
\n" ); document.write( " $\"d%5E2+=+b\"$
\n" ); document.write( " $\"6%5E2+=+b\"$
\n" ); document.write( " $\"b+=+36\"$
\n" ); document.write( "The numbers are 25 and 36
\n" ); document.write( "check:
\n" ); document.write( "The numbers differ by 11 and
\n" ); document.write( "their square roots differ by 1
\n" ); document.write( " \n" ); document.write( "

\n" );