Đáp án:
\(\left[ \begin{array}{l}
m = \frac{{2 + \sqrt {14} }}{2}\\
m = \frac{{2 - \sqrt {14} }}{2}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
{m^2} - 4m + 4 + {m^2} > 0\\
\left| {{x_1}} \right| - \left| {{x_2}} \right| = 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2{m^2} - 4m + 4 > 0\left( {ld} \right)\forall m \in R\\
{\left( {{x_1}} \right)^2} + {\left( {{x_2}} \right)^2} - 2{x_1}{x_2} = 36
\end{array} \right.\\
\to {\left( {{x_1}} \right)^2} + {\left( {{x_2}} \right)^2} + 2{x_1}{x_2} - 4{x_1}{x_2} = 36\\
\to {\left( {{x_1} + {x_2}} \right)^2} - 4{x_1}{x_2} = 36\\
\to 4\left( {{m^2} - 4m + 4} \right) - 4.\left( { - {m^2}} \right) - 36 = 0\\
\to 8{m^2} - 16m - 20 = 0\\
Do: Δ'= 16 + 8.20 = 176\\
\to \left[ \begin{array}{l}
m = \frac{{2 + \sqrt {14} }}{2}\\
m = \frac{{2 - \sqrt {14} }}{2}
\end{array} \right.
\end{array}\)
