Question 70: Let $\mathrm{m}$ be a positive real number, satisfying: for any positive real numbers $\mathrm{x}$ and $\mathrm{y}$, the lengths $\mathrm{x}+\mathrm{y}$, $\sqrt{x^{2}+y^{2}+x y}$, and $m \sqrt{x y}$ of three line segments can form the three sides of some triangle, then the range of values for $m$ is $\qquad$ _.
Question 70, Solution: According to homogeneity, let $\mathrm{y}=1$, then for any positive real number $\mathrm{x}, \mathrm{x}+1, \sqrt{\mathrm{x}^{2}+\mathrm{x}+1}$, and $\mathrm{m} \sqrt{\mathrm{x}}$ can form the three sides of a triangle. Note that $\mathrm{x}+1>\sqrt{\mathrm{x}^{2}+\mathrm{x}+1}$, so the condition is equivalent to: for any $x \in R^{+}$, we have
$$
\begin{array}{l}
|x+1-m \sqrt{x}|\frac{\sqrt{x}}{x+1} \\
\Leftrightarrow \frac{2 m}{m^{2}+1}>\frac{1}{2} \\
\Leftrightarrow m \in(2-\sqrt{3}, 2+\sqrt{3})
\end{array}
$$

Therefore, the range of $\mathrm{m}$ is $(2-\sqrt{3}, 2+\sqrt{3})$.