Question

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Answer 1

a) \(\left\{{}\begin{matrix}a+b=11\\b+c=12\\c+a=2\end{matrix}\right.\)

\(\Rightarrow a+b+b+c+c+a=11+12+2\)

\(\Rightarrow2\left(a+b+c\right)=25\Rightarrow a+b+c=\dfrac{25}{2}\)

\(\Rightarrow\left\{{}\begin{matrix}a=\dfrac{25}{2}-3==\dfrac{19}{2}\\b=\dfrac{25}{2}-2=\dfrac{21}{2}\\c=\dfrac{25}{2}-11=\dfrac{3}{2}\end{matrix}\right.\)

b) \(\left\{{}\begin{matrix}ab=6\\bc=12\\ca=8\end{matrix}\right.\)\(\Rightarrow ab.bc.ca=6.12.8\)

\(\Rightarrow\left(abc\right)^2=576\Rightarrow abc=\pm24\)

\(\Rightarrow\left\{{}\begin{matrix}a=\pm24:12=\pm2\\b=\pm24:8=\pm3\\c=\pm24:6=\pm4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a=2\\b=3\\c=4\end{matrix}\right.\\\left\{{}\begin{matrix}a=-2\\b=-3\\c=-4\end{matrix}\right.\end{matrix}\right.\)