Question 94
Find the minimum value of the expression
$$
E = \sqrt{x^2 + \frac{1}{y^2}} + \sqrt{y^2 + \frac{1}{z^2}} + \sqrt{z^2 + \frac{1}{x^2}},
$$
taken for all $x, y, z \in \mathbb{R}^*$.
$$
E = \sqrt{x^2 + \frac{1}{y^2}} + \sqrt{y^2 + \frac{1}{z^2}} + \sqrt{z^2 + \frac{1}{x^2}},
$$
taken for all $x, y, z \in \mathbb{R}^*$.