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已知,正数x1,x2,x3,x4,x5,x6,同时满足：（X1X2X3X4X5X6）/X1=1,(X1X2X3X4X5X6)/X3=2,(X1X2X3X4X5X6)/X4=4,(X1X2X3X4X5X6)/X5=6,(X1X2X3X4X5X6)/X6=9.求X1+X2+X3+X4+X5+X6的值.
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已知,正数x1,x2,x3,x4,x5,x6,同时满足：（X1X2X3X4X5X6）/X1=1,(X1X2X3X4X5X6)/X3=2,(X1X2X3X4X5X6)/X4=4,(X1X2X3X4X5X6)/X5=6,(X1X2X3X4X5X6)/X6=9.求X1+X2+X3+X4+X5+X6的值.
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答案和解析
（X1X2X3X4X5X6）/X1=1 所以 X1X2X3X4X5X6=X1 所以X2X3X4X5X6=1 (1)
（X1X2X3X4X5X6)/X3=2 所以：X1X2X3X4X5X6=2X3 所以X1X2X4X5X6=2 (2)
(X1X2X3X4X5X6)/X4=4 X1X2X3X4X5X6=4X4 X1X2X3X5X6=4 (3)
(X1X2X3X4X5X6)/X5=6 X1X2X3X4X5X6=6X5 X1X2X3X4X6=6 (4)
(X1X2X3X4X5X6)/X6=9 X1X2X3X4X5X6=9X6 X1X2X3X4X5=9 (5)
(2)/(1) X1=2X3
(3)/(1)X1=4X4
(4)/(1)X1=6X5
(5)/(1)X1=9X6
X1+X2+X3+X4+X5+X6=5/4X1+X2
把x3=1/2x1.x4=1/4x1.带入（1）（2）解出x1 x2 带入即可
（X1X2X3X4X5X6)/X3=2 所以：X1X2X3X4X5X6=2X3 所以X1X2X4X5X6=2 (2)
(X1X2X3X4X5X6)/X4=4 X1X2X3X4X5X6=4X4 X1X2X3X5X6=4 (3)
(X1X2X3X4X5X6)/X5=6 X1X2X3X4X5X6=6X5 X1X2X3X4X6=6 (4)
(X1X2X3X4X5X6)/X6=9 X1X2X3X4X5X6=9X6 X1X2X3X4X5=9 (5)
(2)/(1) X1=2X3
(3)/(1)X1=4X4
(4)/(1)X1=6X5
(5)/(1)X1=9X6
X1+X2+X3+X4+X5+X6=5/4X1+X2
把x3=1/2x1.x4=1/4x1.带入（1）（2）解出x1 x2 带入即可
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