已知X+Y=-4,xy=-12那么(x+1/Y+1)+(y+1/X+1)=

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已知X+Y=-4,xy=-12那么(x+1/Y+1)+(y+1/X+1)=
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已知X+Y=-4,xy=-12那么(x+1/Y+1)+(y+1/X+1)=
已知X+Y=-4,xy=-12那么(x+1/Y+1)+(y+1/X+1)=

已知X+Y=-4,xy=-12那么(x+1/Y+1)+(y+1/X+1)=
x+y=-4
平方
x²+y²+2xy=16
x²+y²=16-2xy=40
原式=[(x+1)²+(y+1)²]/(x+1)(y+1)
=[(x²+y²)+2(x+y)+2]/(xy+x+y+1)
=(40-8+2)/(-12-4+1)
=-34/15

-34/15

原式=x+y+1/x+1/y+2
=-4+2+1/x+1/y
=-2+(x+y)/xy
=-2+1/3
=-5/3

x+y=-4
平方
x²+y²+2xy=16
x²+y²=16-2xy=40
原式=[(x+1)²+(y+1)²]/(x+1)(y+1)
=[(x²+y²)+2(x+y)+2]/(xy+x+y+1)
=(40-8+2)/(-12-4+1)
=-34/15