已知x²-xy-2y²=x-2y,且x-2y≠0,则:(1)x+y=_______(2)若题中x、y满足等式x²+y²-9x+5y+26=0,请确定x、y的值.

Question

已知x²-xy-2y²=x-2y,且x-2y≠0,则:(1)x+y=_______
(2)若题中x、y满足等式x²+y²-9x+5y+26=0,请确定x、y的值.

Answer 1

(1) 将等式变形为 (x+y)(x-2y)=x-2y ,因x-2y≠0,两边除以x-2y得 x+y = 1
(2) 将x=1-y代入方程,得
(1-y)²-9(x+y)+14y+26=0
整理得 y²+6y+9=0 即 (y+3)²=0
故 y= - 3 ,x=1-y = 4