Question

已知ax^3=by^3=cz^3且1\x+1\y+1\z=1,求证：(ax^2+by^2+cz^2)^1\3=a^1\3

Answer 1

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.