document.write( "Question 1209470: Two numbers between 150 and 200 can each be expressed as the sum of two squares in two different ways. Find their difference.
\n" ); document.write( "CC13F #2 \n" ); document.write( "

Algebra.Com's Answer #848900 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Two numbers between 150 and 200 can each be expressed as the sum of two squares in two different ways.
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Make the table of squares of natural numbers between 0 and 200  (not so many opportunities)\r\n" );
document.write( "\r\n" );
document.write( "    0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Make the table of sums of squares between 150 and 200  (not so many opportunities)\r\n" );
document.write( "\r\n" );
document.write( " 100 + 64 = 164\r\n" );
document.write( " 121 + 25 = 146\r\n" );
document.write( " 121 + 36 = 157\r\n" );
document.write( " 121 + 49 = 170\r\n" );
document.write( " 121 + 64 = 185  (**)\r\n" );
document.write( " 121 + 81 = 202\r\n" );
document.write( " 144 + 25 = 169   (*)\r\n" );
document.write( " 144 + 36 = 180\r\n" );
document.write( " 144 + 49 = 193\r\n" );
document.write( " 169 +  0 = 169   (*)\r\n" );
document.write( " 169 +  9 = 178\r\n" );
document.write( " 169 + 16 = 185  (**)\r\n" );
document.write( " 169 + 25 = 194\r\n" );
document.write( " 196 +  0 = 196\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The repeating sums in this list are  \r\n" );
document.write( "\r\n" );
document.write( "    169 = 169 + 0 = 144 + 25   (marked * in the list),\r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( "    185 = 121 + 64 = 169 + 16  (marked ** in the list).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, these two numbers, 169 and 185 are those you are looking for.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Their difference is  185 - 169 = 16.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );