2008x³=2009y³=2010z³ .条件①
2008x²+2009y²+2010z²)的立方根=2008的立方根+2009的立方根+2010的立方根 .条件②
令2008x^3=2009y^3=2010^3=M
可以知道:2008x^2=M/x 2009y^2=M/y 2010z^2=M/z
又(2008x²+2009y²+2010z²)=M(1/x+1/y+1/z)
故:〔M(1/x+1/y+1/z)〕^(1/3)=M^(1/3)*(1/x+1/y+1/z)^(1/3)
同时2008^(1/3)=M^(1/3)/x 2009^(1/3)=M^(1/3)/y
2010^(1/3)=M^(1/3)/z
综合条件二可知:
M^(1/3)*(1/x+1/y+1/z)^(1/3)=M^(1/3)/x+M^(1/3)/y+M^(1/3)/z
消去M^(1/3)可得:
(1/x+1/y+1/z)^(1/3)=1/x+1/y+1/z
这样我们就可以知道结果是
1/x+1/y+1/z=1