document.write( "Question 1141463: solve : x^2 + x = y^2 - 2y , x, y belong to N (integer) \n" ); document.write( "

Algebra.Com's Answer #761999 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"x%5E2%2Bx+=+y%5E2-2y\"$
\n" ); document.write( " $\"x%28x%2B1%29+=+y%28y-2%29\"$
\n" ); document.write( " $\"x%28x%2B1%29-y%28y-2%29+=+0\"$

\n" ); document.write( "The equation is satisfied when x(x+1) and y(y-2) are both 0:

\n" ); document.write( "(1) x=0 and y=0;
\n" ); document.write( "(2) x=0 and y=2;
\n" ); document.write( "(3) x=-1 and y=0; and
\n" ); document.write( "(4) x=-1 and y=2

\n" ); document.write( "Solutions: (0,0), (0,2), (-1,0), (-1,2)

\n" ); document.write( "That does not preclude the possibility of other solutions; it seems unlikely that there would be.

\n" ); document.write( "Entering \"integer solutions to x^2+x=y^2-2y on wolframalpha.com shows only those four solutions.
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