Question

 1 ) tìm các số x, y ,z biết rằng :
 B ) \(\frac{x^3}{8}=\frac{y^3}{64}=\frac{z^3}{216}\)  và x² + y² + z² = 14

Answer 1

\(\frac{x^3}{8}=\frac{y^3}{64}=\frac{z^3}{216}\Rightarrow\left(\frac{x}{2}\right)^3=\left(\frac{x}{4}\right)^3=\left(\frac{x}{6}\right)^3\Rightarrow\frac{x}{2}=\frac{y}{4}=\frac{z}{6}\)

\(\Rightarrow\frac{x^2}{4}=\frac{y^2}{16}=\frac{z^2}{36}=\frac{x^2+y^2+z^2}{4+16+36}=\frac{14}{56}=\frac{1}{4}\)

\(\Rightarrow x^2=1;y^2=4;z^2=9\) 

\(\Rightarrow x=1;y=2;z=3\) hoặc \(x=-1;y=-2;z=-3\)