Đáp án:
\(\left[ \begin{array}{l}
a = 6 \to b = 8,c = 10\\
a = - 6 \to b = - 8,c = - 10
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
2{a^2} + 2{b^2} - 3{c^2} = - 100\\
\frac{a}{3} = \frac{b}{4} = \frac{c}{5} \leftrightarrow \frac{{{a^2}}}{9} = \frac{{{b^2}}}{{16}} = \frac{{{c^2}}}{{25}} = \frac{{2{a^2}}}{{18}} = \frac{{2{b^2}}}{{32}} = \frac{{ - 3{c^2}}}{{ - 75}} = \frac{{2{a^2} + 2{b^2} - 3{c^2}}}{{18 + 32 - 75}} = \frac{{ - 100}}{{ - 25}} = 4\\
\to {a^2} = 9.4 = 36 \leftrightarrow \left[ \begin{array}{l}
a = 6 \to b = 8,c = 10\\
a = - 6 \to b = - 8,c = - 10
\end{array} \right.
\end{array}\)
