b2c b22soabcbisarationalpointonthecirclex2y22Converselyifxandyarerationalnumberssatisfyingx2y22writexandywithacommondenominatorasxabandycbwhereabc2ZThena2c22b2soc2b2b2a2 ID: 467750
b2+c b2=2;so(a=b;c=b)isarationalpointonthecirclex2+y2=2.Conversely ifxandyarerationalnumberssatisfyingx2+y2=2 writexandywithacommondenominatorasx=a=bandy=c=bwherea;b;c2Z.Thena2+c2=2b2