Question

Tìm m để:

x²-2(2m+1)x +m(m+9)<0 vô nghiệm

Answer 1

Answer 2

\(x^2-2\left(2m+1\right)x+m\left(m+9\right)< 0\) vô nghiệm

\(\Leftrightarrow\)\(x^2-2\left(2m+1\right)x+m\left(m+9\right)\ge0\forall x\in R\)

\(\Leftrightarrow\left\{{}\begin{matrix}a>0\\\Delta\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}1>0\left(lđ\right)\\3x^2-5x+1\le0\end{matrix}\right.\)

\(\Rightarrow m\in\left[\dfrac{5-\sqrt{13}}{6};\dfrac{5+\sqrt{13}}{6}\right]\)

Vậy \(\Rightarrow m\in\left[\dfrac{5-\sqrt{13}}{6};\dfrac{5+\sqrt{13}}{6}\right]\) làm cho bpt vô nghiệm