ta có : \(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}\Leftrightarrow\dfrac{x^2}{36}=\dfrac{y^2}{16}=\dfrac{z^2}{9}\)
áp dụng tính chất dãy tỉ số bằng nhau
ta có : \(\dfrac{x^2-y^2-z^2}{36-16-9}=\dfrac{1331}{11}=121\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x^2}{36}=121\\\dfrac{y^2}{16}=121\\\dfrac{z^2}{9}=121\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x^2=4356\\y^2=1936\\z^2=1089\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\pm66\\y=\pm44\\z=\pm33\end{matrix}\right.\)
vậy \(x=\pm66;y=\pm44;z=\pm33\)
Ta có : \(\dfrac{x}{6}=\dfrac{x^2}{36};\dfrac{y}{4}=\dfrac{y^2}{16};\dfrac{z}{3}=\dfrac{z^2}{9}\)
Áp dụng tính chất của dãy tỉ số bằng nhau có :
\(\dfrac{x^2}{36}=\dfrac{y^2}{16}=\dfrac{z^2}{9}=\dfrac{x^2-y^2-z^2}{36-16-9}=\dfrac{1331}{11}=121\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x^2}{36}=121\\\dfrac{y^2}{16}=121\\\dfrac{z^2}{9}=121\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x^2=4356\\y^2=1936\\z^2=1089\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=66\\y=44\\z=33\end{matrix}\right.\)
\(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}\)
\(\Rightarrow\left(\dfrac{x}{6}\right)^2=\left(\dfrac{y}{4}\right)^2=\left(\dfrac{z}{3}\right)^2\)
\(\Rightarrow\dfrac{x^2}{36}=\dfrac{y^2}{16}=\dfrac{z^2}{9}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x^2}{36}=\dfrac{y^2}{16}=\dfrac{z^2}{9}=\dfrac{x^2-y^2-z^2}{36-16-9}=\dfrac{1331}{11}=121\)
Áp dụng tính
