3-ча 1. Determine the ratio of two numbers if the ratio of their arithmetic mean to geometric mean is $25: 24$.
Let $x$ and $y$ be the required numbers. According to the condition, $\frac{x+y}{2}: \sqrt{x y}=25: 24$, i.e., $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{25}{12}$. Let $q=\sqrt{x / y}$. Then $q+\frac{1}{q}=\frac{25}{12}$, i.e., $q^{2}-\frac{25}{12} q+1=0$. Solving this quadratic equation, we find $q_{1}=4 / 3$ and $q_{2}=3 / 4$. Thus, $x: y=16: 9$ or $9: 16$.