已知ax^3=by^3=cz^3,三次根号(ax^2+by^2+cz^2)=三次根号a+三次根号b+三次根号c,求(1/x+1/y+1/z)的值
问题描述：
已知ax^3=by^3=cz^3,三次根号(ax^2+by^2+cz^2)=三次根号a+三次根号b+三次根号c,求(1/x+1/y+1/z)的值
答
(ax^2+by^2+cz^2)^(1/3)=a^(1/3)+b^(1/3)+c^(1/3)(ax^3(1/x+1/y+1/z))^(1/3)=a^(1/3)+b^(1/3)+c^(1/3)x=[a^(1/3)+b^(1/3)+c^(1/3)]/(a(1/x+1/y+1/z)^(1/3)1/x=(a(1/x+1/y+1/z)^(1/3)/[a^(1/3)+b^(1/3)+c^(1/3)] (1)...