Question

Cho \(\dfrac{x}{2}=\dfrac{y}{2}=\dfrac{z}{5}\) và xyz = 810. Tính x + y + z

Answer 1

\(Đặt\) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)

\(\Rightarrow x=2k\)

\(y=3k\)

\(z=5k\)

\(Thay\) \(x=2k;y=3k;z=5k\) vào \(xyz=810\) \(ta\) \(được\):

\(2k\cdot3k\cdot5k=810\)

\(30k^3=810\)

\(k^3=27\)

\(k^3=3^3\)

\(\Rightarrow k=3\)

\(\Rightarrow x=2\cdot3=6\)

\(y=3\cdot3=9\)

\(z=3\cdot5=15\)

\(Từ\) \(đó\)\(ta\) \(tính\) \(được\):\(x+y+z\)

\(\Rightarrow x+y+z=6+9+15\)

\(\Rightarrow x+y+z=30\)