Đáp án:
\(\,\,\left( {x;\,\,y;\,\,z} \right) = \left\{ {\left( {6;\,\,8;\,\,10} \right);\,\,\,\left( { - 6; - 8; - 10} \right)} \right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
x:y:z = 3:4:5\\
\Rightarrow \frac{x}{3} = \frac{y}{4} = \frac{z}{5}\\
\Rightarrow \frac{{{x^2}}}{9} = \frac{{{y^2}}}{{16}} = \frac{{{z^2}}}{{25}} = \frac{{2{x^2} + 2{y^2} - 3{z^2}}}{{2.9 + 2.16 - 3.25}} = \frac{{ - 100}}{{ - 25}} = 4\\
\Rightarrow \left\{ \begin{array}{l}
{x^2} = 4.9 = 36\\
{y^2} = 4.16 = 64\\
{z^2} = 4.25 = 100
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \pm 6\\
y = \pm 8\\
z = \pm 10
\end{array} \right.\\
Vay\,\,\,\left( {x;\,\,y;\,\,z} \right) = \left\{ {\left( {6;\,\,8;\,\,10} \right);\,\,\,\left( { - 6; - 8; - 10} \right)} \right\}.
\end{array}\)
