Question

已知x^2+y^2-2x+2y=-2,求代数式x^2005+x^2006的值

Answer 1

x^2+y^2-2x+2y=-2, x^2+y^2-2x+2y+2=0 x^2-2x+1+y^2+2y+1=0 (x-1)^2+(y+1)^2=0 x-1=0,y+1=0 x=1,y=-1 所以x^2005+x^2006 =1+1 =2