解方程组 xy+x+y=-13 x²+y²=29
问题描述：
解方程组 xy+x+y=-13 x²+y²=29
答
xy+x+y=-13....xy=-13-(x=y)
x2+y2=29.....x2+y2+2xy=29-2*13-2(x+y)=3-2(x+y)
....(x+y)2+2(x+y)-3=0
...(x+y+3)(x+y-1)=0
...1.x+y=-3 xy=-10 或2.x 或2.x+y=1 xy=-14由1.得出x=-5,y=2或x=2，y=-5
答
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答
xy+x+y=-13
xy=-13-(x+y)
x²+y²
=(x+y)²-2xy
=(x+y)²-2[-13-(x+y)]
=(x+y)²+26+2(x+y)=29
(x+y)²+2(x+y)-3=0
(x+y+3)(x+y-1)=0
1:x+y=-3
xy=-10
解得：x=-5 y=2或者x=2 y=5
2:x+y=1
xy=-14
解得：
解得:x=(1+√57)/2 y=(1-√57)/2 或者x=(1-√57)/2 y=(1+√57)/2