알려 진 ax^3=by^3=cz^3 및 1\x+1\y+1\\\z=1,구 증:(ax^2+by^2+cz^2)^1\\\3=a^1\\3+b^1\\3+c^1\3.

알려 진 ax^3=by^3=cz^3 및 1\x+1\y+1\\\z=1,구 증:(ax^2+by^2+cz^2)^1\\\3=a^1\\3+b^1\\3+c^1\3.

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