Question

cho x;y;z thỏa mãn x³/1000=y³/3375=z³/1728 và x-y+z =-49.Khi đó x+y+z=

Answer 1

\(\frac{x^3}{1000}=\frac{y^3}{3375}=\frac{z^3}{1728}\Rightarrow\left(\frac{x}{10}\right)^3=\left(\frac{y}{15}\right)^3=\left(\frac{z}{12}\right)^3\)

\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{12}=\frac{x-y+z}{10-15+12}\left(\text{t/c dãy tỉ số = nhau}\right)=\frac{-49}{7}=-7\)

\(\Rightarrow\frac{x}{10}=-7\Rightarrow x=-7.10=-70\)

\(\Rightarrow\frac{y}{15}=-7\Rightarrow y=-7.15=-105\)

\(\Rightarrow\frac{z}{12}=-7\Rightarrow z=-7.12=-84\)

Vậy x+y+z=(-70)+(-105)+(-84)=-259.