# (Not) just your average problem

Calculus Level 5

\large{ \begin{align} x+y+z=0 \\ x^2+y^2+z^2=1\end{align}}

Consider the curve $$C$$ defined by the two equations above. Find the average value of $$f(x,y,z)=x^2y^2z^2$$ on $$C$$.

Enter the reciprocal of this average.

Inspiration

×