Re: [代數] 解方程式一題

[supermicro ( 超 級 微 小 )]

y-2xy-y^2=0  ... (1)
x-x^2-2xy=0  ... (2)

  (2)-(1)
  (x-y) - (x^2-y^2) = 0 = (x-y)(1-x-y)=0

  (i)  x-y = 0 => y=x 代入(2)
       x-x^2-2x^2 = 0  => x = y = 0 v 1/3

  (ii) 1-x-y = 0 => y=1-x 代入(2)

       x-x^2-2x(1-x) = 0 解得 x = 0 v 1


(x,y) = (0,0) (0,1) (1/3,1/3) (1,0)

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