a) \(2x^2-5x^2+6x+13=0\)
\(\Leftrightarrow-3x^2+6x+13=0\)
\(\Leftrightarrow3x^2-6x-13=0\left(1\right)\)
\(\Delta'=9+39=48>0\Rightarrow\sqrt[]{\Delta'}=4\sqrt[]{3}\)
Pt (1) có 2 nghiệm phân biệt là :
\(\left[{}\begin{matrix}x=\dfrac{3+4\sqrt[]{3}}{3}=1+\dfrac{4\sqrt[]{3}}{3}\\x=\dfrac{3-4\sqrt[]{3}}{3}=1-\dfrac{4\sqrt[]{3}}{3}\end{matrix}\right.\)
b) \(x^2-5x=-4\)
\(\Leftrightarrow x^2-5x+4=0\)
\(\Leftrightarrow x^2-x-4x+4=0\)
\(\Leftrightarrow x\left(x-1\right)-4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)
