已知ax^3=by^3=cz^3,1x+1y+1z,

题目

已知ax^3=by^3=cz^3,1x+1y+1z,
,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何

答案

设ax^3=by^3=cz^3=s^3,
∴(ax^2+by^2+cz^2)^13
=(s^3/x+s^3/y+s^3/z)^1/3
=[s^3(1/x+1/y+1/z)]^1/3
=s
∵a^13+b^13+c^13
=s/x+s/y+s/z
=s(1/x+1/y+1/z)
=s
∴(ax^2+by^2+cz^2)^13=a^13+b^13+c^13.