document.write( "Question 1199579: For the equation $\"%28a-b%29%5E2+%2B+a%5E2+=+289\"$ , a and b are integers and a is more than or equal to 0. List the ordered pairs that occur. \n" ); document.write( "

Algebra.Com's Answer #833518 by greenestamps(13206) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The solutions in integers of the equation x^2+y^2 = 289 are the following:

\n" ); document.write( "(0,17)
\n" ); document.write( "(0,-17)
\n" ); document.write( "(8,15)
\n" ); document.write( "(-8,15)
\n" ); document.write( "(-8,-15)
\n" ); document.write( "(8,-15)

\n" ); document.write( "Since the problem specifies a greater than or equal to 0, a can have any of the values 0, 8, 15, or 17.

\n" ); document.write( "[1] a=0, a-b=17 --> (a,b)=(0,-17)
\n" ); document.write( "[2] a=0, a-b=-17 --> (a,b)=(0,17)
\n" ); document.write( "[3] a=8, a-b=15 --> (a,b)=(8,-7)
\n" ); document.write( "[4] a=8, a-b=-15 --> (a,b)=(8,23)
\n" ); document.write( "[5] a=15, a-b=8 --> (a,b)=(15,7)
\n" ); document.write( "[6] a=15, a-b=-8 --> (a,b)=(15,-23)
\n" ); document.write( "[7] a=17, a-b=0 --> (a,b)=(17,17)

\n" ); document.write( "ANSWER: 7 ordered pairs (a,b): (0,17), (0,-17), (8,-7), (8,23), (15,7), (15,-23), (17, 17)

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

\n" );