\(x^2-2x-3=mx-2m-2\)
\(x^2-2x+2m-mx-1=0\)
\(x^2-\left(m+2\right)x+2m-1=0\)
\(\Delta=\left(m+2\right)^2-4\left(2m-1\right)\)
\(\Delta=m^2+4m+4-8m+4\)
\(\Delta=m^2-4m+8\)
\(\Delta=\left(m-2\right)^2+4>0\)<=> có 2 n0 pb
\(\hept{\begin{cases}xA+xB=-\frac{b}{a}=\frac{m+2}{1}=m+2\\xA.xB=\frac{c}{a}=2m-1\end{cases}}\)
\(xA^2+xB^2=10\)
\(\left(xA+xB\right)^2-2xA.xB=10\)
\(\left(m+2\right)^2-2\left(2m-1\right)=10\)
\(m^2+2m+4-4m+2=10\)
\(m^2-2m+6=10\)
\(m^2-2m-4=0\)
\(\Delta=2^2-\left(-16\right)=20\)
\(\sqrt{\Delta}=2\sqrt{5}\)
\(x_1=\frac{2+2\sqrt{5}}{2}=1+\sqrt{5}\)
\(x_2=\frac{2-2\sqrt{5}}{2}=1-\sqrt{5}\)
2 =3
