\(ab=2;bc=3;ca=54\)
\(\Leftrightarrow ab.bc.ca=2.3.54\)
\(\Leftrightarrow\left(abc\right)^2=324\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(abc\right)^2=18^2\\\left(abc\right)^2=\left(-18\right)^2\end{matrix}\right.\)
+) \(abc=18\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=18:3=6\\b=18:54=\dfrac{1}{3}\\c=18:2=9\end{matrix}\right.\)
+) \(abc=-18\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=\left(-18\right):3=-6\\b=\left(-18\right):54=\dfrac{-1}{3}\\c=\left(-18\right):2=-9\end{matrix}\right.\)
Vậy .....
Ta có:
\(ab.bc.ca=2.3.54\)
\(\Rightarrow\left(abc\right)^2=324=18^2\)
\(\Rightarrow abc=\pm18\)
+, Xét \(abc=-18\) ta có:
\(\left\{{}\begin{matrix}a=abc:bc=-18:3=-6\\b=abc:ac=-18:54=-\dfrac{1}{3}\\c=abc:ab=-18:2=-9\end{matrix}\right.\)
+, Xét \(abc=18\) ta có:
\(\left\{{}\begin{matrix}a=abc:bc=18:3=6\\b=abc:ac=18:54=\dfrac{1}{3}\\c=abc:ab=18:2=9\end{matrix}\right.\)
Vậy............
Chúc bạn học tốt!!!
