\(\left\{\begin{matrix}xy=3\left(1\right)\\xz=4\left(2\right)\\yz=6\left(3\right)\end{matrix}\right.\).Từ \(yz=6\Rightarrow z=\frac{6}{y}\) thay vào (2) ta có:
\(xz=4\Rightarrow x\cdot\frac{6}{y}=4\)\(\Leftrightarrow\frac{6x}{y}=4\Leftrightarrow6x=4y\Leftrightarrow y=\frac{6x}{4}=\frac{3x}{2}\) thay vào (1) ta có:
\(x\cdot\frac{3x}{2}=3\Leftrightarrow\frac{3x^2}{2}=3\Leftrightarrow3x^2=6\Leftrightarrow x^2=2\)
Từ \(\left(1\right)\Rightarrow x^2y^2=9\Rightarrow y^2=\frac{9}{x^2}=\frac{9}{2}\)
Từ \(\left(2\right)\Rightarrow x^2z^2=16\Rightarrow z^2=\frac{16}{x^2}=\frac{16}{2}=8\)
Khi đó \(A=x^2+y^2+z^2=2+\frac{9}{2}+8=\frac{29}{2}\)
