已知x+y=-4,xy=-12,求(x+1/y+1 )+ ( y+1/x+1)的值
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已知x+y=-4,xy=-12,求(x+1/y+1 )+ ( y+1/x+1)的值
要写过程啊
要写过程啊
x+y=-4,则(x+y)²=x²+2xy+y²=(-4)²=16
所以x²+y²=16-2xy=16+24=40
(x+1/y+1 )+ ( y+1/x+1)
=(x+1)²/[(x+1)(y+1)]+(y+1)²/[(x+1)(y+1)]
=[(x+1)²+(y+1)²]/[(x+1)(y+1)]
=(x²+y²+2x+2y+2)/(xy+x+y+1)
=(40+2×(-4)+2)/(-12-4+1)
=34/(-15)
=-34/15
所以x²+y²=16-2xy=16+24=40
(x+1/y+1 )+ ( y+1/x+1)
=(x+1)²/[(x+1)(y+1)]+(y+1)²/[(x+1)(y+1)]
=[(x+1)²+(y+1)²]/[(x+1)(y+1)]
=(x²+y²+2x+2y+2)/(xy+x+y+1)
=(40+2×(-4)+2)/(-12-4+1)
=34/(-15)
=-34/15
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