设2000X^3=2001Y^3=2002Z^3,XYZ＞0 且2000X^2=2001y^2=2002z^2=2000的立方 +2001的立方 +2002的立方,求x分之一+y分之一+z分之一的值.（提示：可设2000x^3=2001y^3=2002z^3=a,则2000x^2=x分之a,则2001y^2=y分之a,2002z^2=z分之a

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设2000X^3=2001Y^3=2002Z^3,XYZ＞0 且2000X^2=2001y^2=2002z^2=2000的立方 +2001的立方 +2002的立方,求x分之一+y分之一+z分之一的值.（提示：可设2000x^3=2001y^3=2002z^3=a,则2000x^2=x分之a,则2001y^2=y分之a,2002z^2=z分之a
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设2000X^3=2001Y^3=2002Z^3,XYZ＞0 且2000X^2=2001y^2=2002z^2=2000的立方 +2001的立方 +2002的立方,求x分之一+y分之一+z分之一的值.（提示：可设2000x^3=2001y^3=2002z^3=a,则2000x^2=x分之a,则2001y^2=y分之a,2002z^2=z分之a
设2000X^3=2001Y^3=2002Z^3,XYZ＞0 且2000X^2=2001y^2=2002z^2=2000的立方 +2001的立方 +2002的立方,求x
分之一+y分之一+z分之一的值.（提示：可设2000x^3=2001y^3=2002z^3=a,则2000x^2=x分之a,则2001y^2=y分之a,2002z^2=z分之a

设2000X^3=2001Y^3=2002Z^3,XYZ＞0 且2000X^2=2001y^2=2002z^2=2000的立方 +2001的立方 +2002的立方,求x分之一+y分之一+z分之一的值.（提示：可设2000x^3=2001y^3=2002z^3=a,则2000x^2=x分之a,则2001y^2=y分之a,2002z^2=z分之a
设2000x3=2001y3=2002z3=k 则2000x2=k/x 2001y2=k/y 2002z2=k/z
2000的立方根=k的立方根/x 2001的立方根=k的立方根/y 2002的立方根=k的立方根/z
由已知可得：（k/x+k/y+k/z)的立方根=k的立方根/x + k的立方根/y +k的立方根/z
所以就可以得到(1/x+1/y+1/z)的立方根=1/x+1/y+1/z
又因为xyz>0,所以只能是x>0 y>0 z>0
所以1/x+1/y+1/z=1

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