x^2+y^2+x+y=18x^2+xy+y^2=19越快越好!讲清楚!
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x^2+y^2+x+y=18x^2+xy+y^2=19越快越好!讲清楚!
x^2+y^2+x+y=18
x^2+xy+y^2=19
越快越好!
讲清楚!
x^2+y^2+x+y=18x^2+xy+y^2=19越快越好!讲清楚!
此方程组共有四组分别是:
x=2,y=3或x=3,y=2
x= —2+√7,y= —2 —√7或x=—2 —√7,y= —2+√7
将这两条方程改写成以下形式:
(x+y)^2 —2xy +(x+y)=18
(x+y)^2 —xy =19
令x+y=T,xy=U.即用换元法,把x+y,xy都看成整体.方程变为:
T^2 —2U + T =18 (1)
T^2 —U =19 (2)
(2)式可写为U=T^2 —19,代入(1)式,并整理,得到
T^2-T-20=0
解得T=5或 —4
所以x+y=5,或x+y= —4
当x+y=5时,xy=6
解得x=2,y=3或x=3,y=2
当x+y= —4时,xy= —3
解得 x= —2+√7,y= —2 —√7或x=—2 —√7,y= —2+√7
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