解方程组:1、x^2-2xy-y^2=1 2、根号下(xy+3)=x

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/18 13:23:15

√(xy+3)=x
xy+3=x^2
所以y=(x^2-3)/x
代入x^2-2xy-y^2=1
x^2-2(x^2-3)-(x^2-3)^2/x^2=1
-x^2+6-(x^2-3)^2/x^2=1
-x^4+6x^2-x^4+6x^2-9=x^2
2x^4-11x^2+9=0
(2x^2-9)(x^2-1)=0
x^2=1,x^2=9/2
x=±1,x=±3√2/2
y=(x^2-3)/x
所以x=1,y=-2
x=-1,y=2
x=3√2/2,y=√2/2
x=-3√2/2,y=-√2/2
经检验,x小于0的解舍去
所以x=1,y=-2
或x=3√2/2,y=√2/2

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