x²+XY+Y=14,Y²+XY+X=28求x+y的值
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x²+XY+Y=14,Y²+XY+X=28求x+y的值x²+XY+Y=14,Y²+XY+X=28求x+y的值x²+XY+Y=14,Y²+XY
x²+XY+Y=14,Y²+XY+X=28求x+y的值
x²+XY+Y=14,Y²+XY+X=28求x+y的值
x²+XY+Y=14,Y²+XY+X=28求x+y的值
两式相加
x²+2xy+y²+x+y=42
(x+y)²+(x+y)-42=0
(x+y+7)(x+y-6)=0
x+y=-7 或x+y=6
两个式子相加得:
x²+2xy+y²+x+y=42,
即:﹙x+y﹚²+﹙x+y﹚-42=0,
∴﹙x+y﹚²-6﹙x+y﹚+7﹙x+y﹚-42
=﹙x+y﹚﹙x+y-6﹚+7﹙x+y-6﹚
=﹙x+y-6﹚﹙x+y+7﹚=0
∴x+y=6或x+y=-7
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