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瑙f柟绋嬬粍:x虏-xy+y虏=3,2x虏-xy-y虏=5
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瑙f柟绋嬬粍:x虏-xy+y虏=3,2x虏-xy-y虏=5
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解二元二次方程组:x^2-xy+y^2=3,2x^2-xy-y^2=5
x^2-xy+y^2=3①
2x^2-xy-y^2=5②
①×5得
5x^2-5xy+5y^2=15
②×3得
6x^2-3xy-3y^2=15
两式子相减得
x^2+2xy-8y^2=0
(x+4y)(x-2y)=0
x=2y或者x=-4y
当x=2y时
由①式有
4y^2-2y^2+y^2=3
3y^2=3
y=±1
此时x=2,y=1或者x=-2,y=-1
如果x=-4y,代入②式得
16y^2+4y^2+y^2=3
y^2=1/7
y=±根号7/7
x=4根号7/7,y=-根号7/7
或者x=-4根号7/7,y=根号7/7
x^2-xy+y^2=3①
2x^2-xy-y^2=5②
①×5得
5x^2-5xy+5y^2=15
②×3得
6x^2-3xy-3y^2=15
两式子相减得
x^2+2xy-8y^2=0
(x+4y)(x-2y)=0
x=2y或者x=-4y
当x=2y时
由①式有
4y^2-2y^2+y^2=3
3y^2=3
y=±1
此时x=2,y=1或者x=-2,y=-1
如果x=-4y,代入②式得
16y^2+4y^2+y^2=3
y^2=1/7
y=±根号7/7
x=4根号7/7,y=-根号7/7
或者x=-4根号7/7,y=根号7/7
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