[tex]2lgx = lg(4x - 3)[/tex]
Condiții de existență :
[tex]x>0[/tex]
[tex]4x-3>0[/tex]
[tex]lg {x}^{2} = lg(4x - 3)[/tex]
[tex] {x}^{2} = 4x - 3[/tex]
[tex] {x}^{2} - 4x + 3 = 0[/tex]
[tex]M1) {x}^{2} - 4x + 3 = 0[/tex]
[tex] {x}^{2} - 3x - x + 3 = 0[/tex]
[tex]x(x - 3) - (x - 3) = 0[/tex]
[tex](x - 3)(x - 1) = 0[/tex]
[tex]x - 3 = 0 = > x_{1} = 3\:verifica \: conditiile[/tex]
[tex]x - 1 = 0 = > x_{2}= 1\:verifica\:conditiile[/tex]
[tex]S=\left\{1,3\right\}[/tex]
[tex]M2) {x}^{2} - 4x + 3 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = - 4[/tex]
[tex]c = 3[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 4)}^{2} - 4 \times 1 \times 3[/tex]
[tex]\Delta = 16 - 12[/tex]
[tex]\Delta = 4[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - ( - 4) \pm \sqrt{4} }{2 \times 1} = \frac{4 \pm2}{2} [/tex]
[tex]x_{1} = \frac{4 + 2}{2} = \frac{6}{2} = 3\:verifica\:conditiile[/tex]
[tex]x_{2} = \frac{4 - 2}{2} = \frac{2}{2} = 1\:verifica\:conditiile[/tex]
[tex]S=\left\{1,3\right\}[/tex]
