document.write( "Question 1209332: For the equation (a-b)^2 + a^2 = 625, a and b are integers and a≥0. List the ordered pairs that occur. \n" ); document.write( "

Algebra.Com's Answer #848387 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The (unordered) pairs of non-negative integers m and n that satisfy the equation m^2+n^2 = 625 are (0,25), (7,24), and (15,20).

\n" ); document.write( "In this problem we need to have (a-b)^2+a^2 = 625, with a greater than or equal to 0.

\n" ); document.write( "So a can be any of the six numbers in those unordered pairs; and, since (a-b) is squared, (a-b) can be positive or negative.

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document.write( "    a  (a-b)  b  ordered pair (a,b)\r\n" );
document.write( "  ----------------------------------\r\n" );
document.write( "    0   25  -25  (0,-25)\r\n" );
document.write( "    0  -25   25  (0,25)\r\n" );
document.write( "    7   24  -17  (7,-17)\r\n" );
document.write( "    7  -24   31  (7,31)\r\n" );
document.write( "   15   20   -5  (15,-5)\r\n" );
document.write( "   15  -20   35  (15,35)\r\n" );
document.write( "   20   15    5  (20,5)\r\n" );
document.write( "   20  -15   35  (20,35)\r\n" );
document.write( "   24    7   17  (24,17)\r\n" );
document.write( "   24   -7   31  (24,31)\r\n" );
document.write( "   25    0   25  (25,0)

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