X+1/X=2a Y+1/Y=-2a(a>0且x+y=/0)

来源：百度知道编辑：UC知道时间：2024/06/04 11:36:25

X+1/X=2a Y+1/Y=-2a(a>0且x+y=/0)..求xy 减根号下(x^2+1)(y^2+1)

X+1/X=2a Y+1/Y=-2a
x+y+1/x+1/y=0
(x+y)+(x+y)/xy=0
(x+y)(1+1/xy)=0
因为x+y=/0
所以1+1/xy=0
xy=-1

X+1/X=2a Y+1/Y=-2a
(x+1/x)(y+1/y)=-4a^2
xy+1/xy+x/y+y/x=-4a^2
-1-1+(x^2+y^2)/xy=-4a^2
x^2+y^2=4a^2-2
(x^2+1)(y^2+1)
=(xy)^2+x^2+y^2+1
=2+4a^2-2
a>0
所以根号下(x^2+1)(y^2+1)=2a

所以xy 减根号下(x^2+1)(y^2+1)
=-1-2a

X+1/X=2a Y+1/Y=-2a
两式相加
得X+1/X+Y+1/Y=0
则(X+Y)(1+1/XY)=0
已知x+y=/0
所以1+1/XY=0
解得XY=-1

(x^2+1)(y^2+1)
=(x^2+1)(y^2+1)/xy *xy
=(x+1/x)(y+1/y) *xy
=2a*(-2a)*xy
所以
xy-根号下(x^2+1)(y^2+1)
=xy-2a根号下(-xy)
=-1-2a

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