# Integral solutions only!!

**Algebra**Level 5

*positive* integral solutions of the equation \[\begin{vmatrix} { y }^{ 3 }+1 & { y }^{ 2 }z & { y }^{ 2 }x \\ y{ z }^{ 2 } & { z }^{ 3 }+1 & { z }^{ 2 }x \\ y{ x }^{ 2 } & { x }^{ 2 }z & { x }^{ 3 }+1 \end{vmatrix}=11\]