解方程组 x2 -2xy -y2 =1 2x2 -5xy -3y2 =0

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解方程组x2-2xy-y2=12x2-5xy-3y2=0解方程组x2-2xy-y2=12x2-5xy-3y2=0解方程组x2-2xy-y2=12x2-5xy-3y2=0x^2-2xy-y^2=1.12

解方程组 x2 -2xy -y2 =1 2x2 -5xy -3y2 =0
解方程组 x2 -2xy -y2 =1 2x2 -5xy -3y2 =0

解方程组 x2 -2xy -y2 =1 2x2 -5xy -3y2 =0
x^2 -2xy -y^2 =1 .1
2x^2 -5xy -3y^2 =0.2
由2式得
(2x+y)(x-3y)=0
x=-y/2或x=3y
将x=-y/2代入1式得
y^2/4+y^2-y^2=1
y^2=4
y=±2
当y=2时
x=-y/2=-1
当y=-2时
x=-y/2=1
将x=3y代入1式得
9y^2-6y^2-y^2=1
2y^2=1
y=±√2/2
当y=√2/2时
x=3y=3√2/2
当y=-√2/2时
x=3y=-3√2/2
所以x=-3√2/2,y=-√2/2
或x=3√2/2,y=√2/2
或x=2,y=-1
或x=-2,y=1

2x²-5xy-3y²=(x-3y)(2x+y)=0
x=3y或y=-2x
x=3y
代入x²-2xy-y²=1
9y²-6y²-y²=1
y²=1/2
y=±√2/2
x=3y
y=-2x
代入x²-2xy-y²=1
...

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2x²-5xy-3y²=(x-3y)(2x+y)=0
x=3y或y=-2x
x=3y
代入x²-2xy-y²=1
9y²-6y²-y²=1
y²=1/2
y=±√2/2
x=3y
y=-2x
代入x²-2xy-y²=1
x²+4x²-4x²=1
x²=1
x=±1
y=-2x
所以
x=3√2/2,y=√2/2
x=-3√2/2,y=-√2/2
x=1,y=-2
x=-1,y=2

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