Cho \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\) và \(xyz=810\)
Tìm x; y; z
Bài làm
Ta có:
\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)
\(\Rightarrow\frac{x^3}{8}=\frac{y^3}{27}=\frac{z^3}{64}=\frac{xyz}{2.3.4}=\frac{810}{24}=33,75\)
=> x3 = 33,75.8 = 270 => x = \(\sqrt[3]{270}\)
y3 = 33,75.27 = 911,25 => y = \(\sqrt[3]{911,25}\)
z3 = 33,75.64 = 2160 => z = \(\sqrt[3]{2160}\)
Vậy x = \(\sqrt[3]{270}\)
y = \(\sqrt[3]{911,25}\)
\(z=\sqrt[3]{2160}\)