解方程组 (x+y)^2-3(x+y)=54 (x-y)^2-5(x-y)=14

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/11 06:27:03

(x+y)^2-3(x+y)=54 (1)
(x-y)^2-5(x-y)=14 (2)
由(1)得(x+y-9)(x+y+6)=0
∴x+y=9 x+y=-6
由(2)得(x-y-7)(x-y+2)=0
∴x-y=7 x-y=-2
∴可组成四个方程组
x+y=9 x+y=9 x+y=-6 x+y=-6
x-y=7 x-y=-2 x-y=7 x-y=-2
∴x=8 x=7/2 x=1/2 x=-4
y=1 y=11/2 y=-13/2 y=-2

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