[tex] \sqrt{2 {x}^{2} - 6x + 5} = x - 1 \: |{( \: )}^{2} [/tex]
[tex]2 {x}^{2} - 6x + 5 \geqslant 0[/tex]
[tex]x - 1 \geqslant 0 = > x \geqslant 1[/tex]
[tex]2 {x}^{2} - 6x + 5 = {(x - 1)}^{2} [/tex]
[tex]2 {x}^{2} - 6x + 5 = {x}^{2} - 2x + 1[/tex]
[tex]2 {x}^{2} - {x}^{2} - 6x + 2x + 5 - 1 = 0[/tex]
[tex] {x}^{2} - 4x + 4 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = - 4[/tex]
[tex]c = 4[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 4)}^{2} - 4 \times 1 \times 4[/tex]
[tex]\Delta = 16 - 16 = 0 = > \exists \: x_{1} = \: x_{2}[/tex]
[tex]x_{1} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - ( - 4) + \sqrt{0} }{2 \times 1} = \frac{4 + 0}{2} = \frac{4}{2} = 2 \: verifica \: conditiile[/tex]
