Đáp án:
b) m=3
Giải thích các bước giải:
\(\begin{array}{l}
a)Thay:m = 1\\
Pt \to {x^2} - 6x + 5 = 0\\
\to \left( {x - 1} \right)\left( {x - 5} \right) = 0\\
\to \left[ \begin{array}{l}
x = 1\\
x = 5
\end{array} \right.\\
b)Xét:\Delta \ge 0\\
\to {m^2} + 10x + 25 - 4\left( { - m + 6} \right) \ge 0\\
\to {m^2} + 10x + 25 + 4m - 24 \ge 0\\
\to {m^2} + 14m + 1 \ge 0\\
\to {m^2} + 14m + 49 - 48 \ge 0\\
\to {\left( {m + 7} \right)^2} \ge 48\\
\to \left[ \begin{array}{l}
m \ge - 7 + 4\sqrt 3 \\
m \le - 7 - 4\sqrt 3
\end{array} \right.\\
Có:{x_1}^2{x_2} + {x_1}{x_2}^2 = 24\\
\to {x_1}{x_2}\left( {{x_1} + {x_2}} \right) = 24\\
\to \left( {6 - m} \right)\left( {m + 5} \right) = 24\\
\to - {m^2} + m + 30 = 24\\
\to - {m^2} + m + 6 = 0\\
\to \left( {3 - m} \right)\left( {m + 2} \right) = 0\\
\to \left[ \begin{array}{l}
m = 3\left( {TM} \right)\\
m = - 2\left( l \right)
\end{array} \right.
\end{array}\)
