If x, y, z are three real numbers with the sa | vedclass

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(B) Since $x, y, z$ have the same sign,the ratios $\frac{x}{y}, \frac{y}{z}, 	ext{ and } \frac{z}{x}$ are all positive.Applying the Arithmetic Mean-G

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$[3, +\infty)$

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(B) Since $x, y, z$ have the same sign,the ratios $\frac{x}{y}, \frac{y}{z}, 	ext{ and } \frac{z}{x}$ are all positive.Applying the Arithmetic Mean-Geometric Mean $(AM \ge GM)$ inequality for these three positive numbers:$\frac{\frac{x}{y} + \frac{y}{z} + \frac{z}{x}}{3} \ge \sqrt[3]{\frac{x}{y} \cdot \frac{y}{z} \cdot \frac{z}{x}}$$\frac{x}{y} + \frac{y}{z} + \frac{z}{x} \ge 3 \cdot \sqrt[3]{1}$$\frac{x}{y} + \frac{y}{z} + \frac{z}{x} \ge 3$Thus,the value lies in the interval $[3, +\infty)$.

If $x, y, z$ are three real numbers with the same sign,then the value of $\frac{x}{y} + \frac{y}{z} + \frac{z}{x}$ lies in which interval?

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