[tex]\it lg^2x-3lgx-c=0\ \ \ \ \ (*)\\ \\ x=10\ \stackrel{(*)}{\Longrightarrow}\ lg^210-3lg10+c=0 \Rightarrow 1-3+c=0 \Rightarrow -2+c=0 \Rightarrow c=2[/tex]
Așadar, avem de rezolvat :
[tex]\it lg^2x-3lgx+2=0 \Rightarrow lg^2x-lgx-2lgx+2=0 \Rightarrow \\ \\ \Rightarrow lgx(lgx-1)-2(lgx-1)=0 \Rightarrow (lgx-1)(lgx-2)=0 \Rightarrow \\ \\ \Rightarrow \begin{cases} \it lgx-1=0 \Rightarrow lgx=1 \Rightarrow x_1=10\\ \\ \it lgx-2=0 \Rightarrow lgx=2 \Rightarrow x=10^2 \Rightarrow x_2=100\end{cases}[/tex]
