If `y z+z x+x y=12 ,w h e r ex ,y ,z` are positive values, find the greatest value of `x y zdot`

Explanation

To find the greatest value of \( xyz \) given the equation \( yz + zx + xy = 12 \) where \( x, y, z \) are positive values, we can use the Arithmetic Mean-Geometric Mean (AM-GM) inequality.

### Step-by-Step Solution:

1. **Apply the AM-GM Inequality**:
According to the AM-GM inequality, for any non-negative numbers \( a, b, c \):
\[
\frac{a + b + c}{3} \geq \sqrt[3]{abc}
...