Ta có:
$\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$
$\to \dfrac{2(x-1)}{4} = \dfrac{3(y-2)}{9} = \dfrac{-(z-3)}{-4}$
$\to \dfrac{2x-2}{4} = \dfrac{3y-6}{9} = \dfrac{3 - z}{-4}$
Áp dụng tính chất dãy tỉ số bằng nhau, ta được:
$\dfrac{2x-2}{4} = \dfrac{3y-6}{9} = \dfrac{3 - z}{-4} = \dfrac{2x - 2 + 3y - 6 + 3 - z}{4 + 9 - 4} = \dfrac{(2x + 3y - z) - 5}{9} = \dfrac{50 - 5}{9} = 5$
+) $\dfrac{x-1}{2} = 5 \to x - 1 = 10 \to x = 11$
+) $\dfrac{y-2}{3} = 5 \to y - 2 = 15 \to y = 17$
+) $\dfrac{z-3}{4} = 5 \to z - 3 = 20 \to z = 23$
