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Use the AGM inequality to find the minimum of \[ x+y+z \] over all positive numbers \( x, y, z \) ...
Use the AGM inequality to find the minimum of \[ x+y+z \] over all positive numbers \( x, y, z \) such that \( (x+y)(y+z)(z+x)=1 \). Hint: use AGM with 3 numbers \( x+y, y+z, z+x \).
![Use the AGM inequality to find the minimum of
\[
x+y+z
\]
over all positive numbers \( x, y, z \) such that \( (x+y)(y+z)(z+x](https://media.cheggcdn.com/media/bc6/bc6e0001-6a51-4c2b-bc0e-aa45fa8bed65/phpnSgVvf)