Toán Lớp 10: x^2-2x+3m-2=0 tìm m thỏa mãn x1<1
Toán Lớp 10: x^2-2x+3m-2=0 tìm m thỏa mãn x1<1
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\to 1 – 3m + 2 > 0\\
\to 3 – 3m > 0\\
\to 1 > m\\
Vi – et:\left\{ \begin{array}{l}
{x_1} + {x_2} = 2\\
{x_1}{x_2} = 3m – 2
\end{array} \right.\\
{x_1} < 1 < {x_2}\\
\to \left\{ \begin{array}{l}
{x_1} – 1 < 0\\
{x_2} – 1 > 0
\end{array} \right.\\
\to \left( {{x_1} – 1} \right)\left( {{x_2} – 1} \right) < 0\\
\to {x_1}{x_2} – \left( {{x_1} + {x_2}} \right) + 1 < 0\\
\to 3m – 2 – 2 + 1 < 0\\
\to 3m < 3\\
\to m < 1\\
KL:1 > m
\end{array}\)