解方程组:x²+2xy+y²=1 2x²-xy=0

解方程组:x²+2xy+y²=1 2x²-xy=0
解方程组:x²+2xy+y²=1 2x²-xy=0

解方程组:x²+2xy+y²=1 2x²-xy=0

x²+2xy+y²=1 2x²-xy=0
(x+y)^2=1 x(2-y)=0
x=0 y=+-1
y=2 x=-1或－3

x²+2xy+y²=1
(x+y)²=1
(x+y)²-1²=0
(x+y-1)(x+y+1)=0
x+y-1=0 or x+y+1=0
x=1-y or x=-1-y


当x=1-y ,2(1-y)²...

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x²+2xy+y²=1
(x+y)²=1
(x+y)²-1²=0
(x+y-1)(x+y+1)=0
x+y-1=0 or x+y+1=0
x=1-y or x=-1-y


当x=1-y ,2(1-y)²-(1-y)y=0
2-4y+2y²-y+y²=0
3y²-5y+2=0
y=1 或 y=2/3
当y=1,x=1-1
x=0
当 y=2/3,x=1-2/3
x=1/3

当x=-1-y, 2(-1-y)²-(-1-y)y=0
2+4y+2y²+y+y²=0
3y²+5y+2=0
y=-1 或 y=-2/3
当y=-1,x=1-(-1)
x=-2
当 y=-2/3,x=1-(-2/3)
x=-5/3
∴ x=0,y=1和x=1/3,y=2/3和x=-2,y=-1和x=-5/3,y=-2/3

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