\(\Delta=b^2-4ac=\left(-48\right)^2-4.1.\left(-25\right)=2400>0\)
do đó pt có 2 nghiệm phân biệt là:
\(•x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{48-\sqrt{2400}}{2}=24-10\sqrt{6}\\ •x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{48+\sqrt{2400}}{2}=24+10\sqrt{6}\)
\(x^2-48x-25=0\)
\(\Leftrightarrow x^2-2.x.24+24^2-601=0\)
\(\Leftrightarrow\left(x-24\right)^2-601=0\)
\(\Leftrightarrow\left(x-24\right)^2=601\)
\(\Leftrightarrow x-24=\sqrt{601}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-24=\sqrt{601}\\x-24=-\sqrt{601}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=24+\sqrt{601}\\x=24-\sqrt{601}\end{matrix}\right.\)
