$\frac{y^3+z^3}{x y z}=2$\n\nLet $a, b$ be the two terms whose arithmetic mean is $x$\n\n\n \nAnd $y, z$ be geometric mean hence $a, y, z, b$ are in G.P.\n\n$\therefore b=a \cdot r^3$ where $r$ is the common ratio of the above G.P.\n\n\n \nNow where $y=a\left(\frac{b}{a}\right)^{1 / 3}$ and $z=a\left(\frac{b}{a}\right)^{2 / 3}$\n\nNow hence $\frac{y^2+z^2}{x y \pi}=\frac{\left[a\left(\frac{b}{a}\right)^{2 / 3}\right]^3+\left[a\left(\frac{b}{a}\right)^{2 / 3}\right]^3}{\frac{a+b}{2} \times a\left(\frac{b}{a}\right)^{1 / 3} \times a\left(\frac{b}{a}\right)^{2 / 3}}$\n\n\n