Đáp án:
\(\left[ \begin{array}{l}
m = - \dfrac{7}{2}\\
m = - \dfrac{{11}}{2}\\
m = - \dfrac{{17}}{4}\\
m = - \dfrac{{19}}{4}
\end{array} \right.\)
Giải thích các bước giải:
Để phương trình có 2 nghiệm phân biệt
\(\begin{array}{l}
\to \Delta ' > 0\\
\to {m^2} + 10m + 25 - 2m - 9 > 0\\
\to {m^2} + 8m + 16 > 0\\
\to {\left( {m + 4} \right)^2} > 0\\
\to m + 4 \ne 0\\
\to m \ne - 4\\
\to \left[ \begin{array}{l}
x = m + 5 + \sqrt {{{\left( {m + 4} \right)}^2}} \\
x = m + 5 - \sqrt {{{\left( {m + 4} \right)}^2}}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = m + 5 + m + 4\\
x = m + 5 - m - 4
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 2m + 9\\
x = 1
\end{array} \right.\\
Vi - et:\left\{ \begin{array}{l}
{x_1} + {x_2} = 2m + 10\\
{x_1}{x_2} = 2m + 9
\end{array} \right.\\
Có:{x_1} - 2\sqrt {{x_2}} = 0\\
\to {x_1} = 2\sqrt {{x_2}} \\
\to {x_1}^2 = 4{x_2}^2\\
\to \left[ \begin{array}{l}
4{m^2} + 36m + 81 = 4.1\\
1 = 4\left( {4{m^2} + 36m + 81} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
4{m^2} + 36m + 77 = 0\\
16{m^2} + 144m + 323 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
m = - \dfrac{7}{2}\\
m = - \dfrac{{11}}{2}\\
m = - \dfrac{{17}}{4}\\
m = - \dfrac{{19}}{4}
\end{array} \right.
\end{array}\)
