Đáp án: $x=3, y=4, z=5$
Giải thích các bước giải:
Ta có:
$\dfrac{3}{x-6}=\dfrac{4}{y-8}=\dfrac{5}{z-10}$
$\to \dfrac{x-6}{3}=\dfrac{y-8}{4}=\dfrac{z-10}{5}$
$\to \dfrac{x}{3}-2=\dfrac{y}{4}-2=\dfrac{z}{5}-2$
$\to \dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=k$
$\to x=3k, y=4k, z=5k$
$\to xyz=3k.4k.5k=60k^3$
Mà $xyz=60\to 60k^3=60\to k^3=1\to k=1$
$\to x=3, y=4, z=5$