Ta có:
\(xy.yz.zx=2.3.54\)
\(\Leftrightarrow x^2.y^2.z^2=324\)
\(\Leftrightarrow\left(xyz\right)^2=324\)
\(\Leftrightarrow\left(xyz\right)^2=18^2=\left(-18\right)^2\)
+ Khi \(\left(xyz\right)^2=18^2\Leftrightarrow xyz=18\)
Vậy \(\left\{{}\begin{matrix}x=18:3=6\\y=18:54=\dfrac{1}{3}\\z=18:2=9\end{matrix}\right.\)
+ Khi \(\left(xyz\right)^2=\left(-18\right)^2\Leftrightarrow xyz=-18\)
Vậy \(\left\{{}\begin{matrix}x=\left(-18\right):3=-6\\y=\left(-18\right):54=-\dfrac{1}{3}\\z=\left(-18\right):2=-9\end{matrix}\right.\)
Ta có: xy=2; yz=3; zx=54 => xy.yz.zx=2.3.54=324 => (xyz)2 = 324 =>xyz=18 hoặc xyz=-18 * nếu xyz=18 => x= xyz ÷ yz =18÷3=6 y=xy÷x= 2÷6=1/3 z=xyz÷x÷y=18÷6÷1/3=9* nếu xyz= -18 Tương tự ta có x=-6 ; y=-1/3 ; z=-9 Vậy : x=6 y=1/3 z=9 hoặc x=-6 y=-1/3 z=-9
\(\left\{{}\begin{matrix}xy=2\\yz=3\\xz=54\end{matrix}\right.\)
\(\Rightarrow xy.yz.xz=2.3.54\)
\(\Rightarrow x^2y^2z^2=324\)
\(\Rightarrow\left(xyz\right)^2=324\)
\(\Rightarrow xyz=\pm18\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}z=18:2=9\\x=18:3=6\\y=18:54=\dfrac{1}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}z=-18:2=-9\\x=-18:3=-6\\y=-18:54=-\dfrac{1}{3}\end{matrix}\right.\end{matrix}\right.\)
