Explicație pas cu pas:
x, y, z ∈ R
[tex]\frac{x}{3} = \frac{y}{4} = \frac{z}{7} = k \\ [/tex]
[tex]x = 3k \\ y = 4k \\ z = 7k[/tex]
[tex]xyz = (3k)(4k)(7k) = 84{k}^{3}[/tex]
[tex]xyz = 1344[/tex]
[tex] \implies 84{k}^{3} = 1344 [/tex]
[tex]{k}^{3} = 16 = {2}^{4}\iff k = 2\sqrt[3]{2} [/tex]
[tex]x = 3\cdot2\sqrt[3]{2} = 6\sqrt[3]{2} \\ y = 4\cdot2\sqrt[3]{2} = 8\sqrt[3]{2} \\ z = 7\cdot2\sqrt[3]{2} = 14\sqrt[3]{2}[/tex]
