1) \(x^2-5x-6=0\)
\(< =>x^2+x-6x-6=0\)
\(< =>x\left(x+1\right)-6\left(x+1\right)=0\)
\(< =>\left(x-6\right)\left(x+1\right)=0\)
\(< =>\left[{}\begin{matrix}x=6\\x=-1\end{matrix}\right.\)
a , de phuong trinh co 2 nghiem trai dau thi
\(\left\{{}\begin{matrix}\Delta\ge0\\x_1.x_2\le0\end{matrix}\right.< =>\left\{{}\begin{matrix}4m^2-4\left(2m-1\right)\ge0\\2m-1\le0\end{matrix}\right.\)
\(< =>\left\{{}\begin{matrix}4m^2-8m+4m\ge0\\m\le\dfrac{1}{2}\end{matrix}\right.\)
\(< =>\left\{{}\begin{matrix}\left(m-1\right)^2\ge0\\m\le\dfrac{1}{2}\end{matrix}\right.\)
\(< =>m\le\dfrac{1}{2}\)
b, Theo he thuc viet thi : \(\left\{{}\begin{matrix}x_1+x_2=2m\\x_1.x_2=2m-1\end{matrix}\right.\)khi do :
pt \(< =>2\left(x_1^2+2x_1x_2+x_2^2\right)-9x_1x_2=27\)
\(< =>2\left(x_1+x_2\right)^2-9x_1x_2-27=0\)
\(< =>8m^2-18m-18=0\)
\(< =>4m^2-9m-9=0\)
\(< =>\left(2m\right)^2-2.2m.\dfrac{9}{4}+\dfrac{81}{16}-9-5\dfrac{1}{6}=0\)
\(< =>\left(2m-\dfrac{9}{4}\right)^2=14\dfrac{1}{6}\)
\(< =>\left(2m-\dfrac{9}{4}\right)^2=\dfrac{85}{6}\)
\(< =>\left[{}\begin{matrix}m=\dfrac{\sqrt{\dfrac{85}{6}}+\dfrac{9}{4}}{2}\\m=\dfrac{-\sqrt{\dfrac{85}{6}}+\dfrac{9}{4}}{2}\end{matrix}\right.\)
doi chieu dieu kien nua nhe
