giải pt -m bình + 5m -2=0

Đáp án:

$ \left[\begin{array}{l} m=\dfrac{5-\sqrt{17}}{2} \\ m=\dfrac{5+\sqrt{17}}{2}\end{array} \right..$

Giải thích các bước giải:

$-m^2+5m-2=0\\ \Leftrightarrow -m^2+2.\dfrac{5}{2}.m-\dfrac{25}{4}+\dfrac{17}{4}=0\\ \Leftrightarrow -\left(m-\dfrac{5}{2}\right)^2+\dfrac{17}{4}=0\\ \Leftrightarrow \left(\dfrac{\sqrt{17}}{2}\right)^2-\left(m-\dfrac{5}{2}\right)^2=0\\ \Leftrightarrow \left(\dfrac{\sqrt{17}}{2}+m-\dfrac{5}{2}\right) \left(\dfrac{\sqrt{17}}{2}-m+\dfrac{5}{2}\right)=0\\ \Leftrightarrow \left(m+\dfrac{\sqrt{17}-5}{2}\right) \left(-m+\dfrac{\sqrt{17}+5}{2}\right)=0\\ \Leftrightarrow \left[\begin{array}{l} m+\dfrac{\sqrt{17}-5}{2}=0 \\ -m+\dfrac{\sqrt{17}+5}{2}=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} m=\dfrac{5-\sqrt{17}}{2} \\ m=\dfrac{5+\sqrt{17}}{2}\end{array} \right..$