[tex]a) \sqrt{2x - 1} = 3[/tex]
Condiția de existență :
[tex]2x - 1 \geqslant 0[/tex]
[tex] \sqrt{2x - 1} = 3 \: | {( \: \: )}^{2} [/tex]
[tex]2x - 1 = 9[/tex]
[tex]2x = 9 + 1[/tex]
[tex]2x = 10 \: | \div 2[/tex]
[tex]x = 5 \: \: verifica \: conditia[/tex]
[tex]c) \sqrt{2x + 3} = 4x[/tex]
Condiția de existență :
[tex]2x + 3 \geqslant 0[/tex]
[tex] \sqrt{2x + 3} = 4x \: | {( \: \: )}^{2} [/tex]
[tex]2x + 3 = 16 {x}^{2} [/tex]
[tex]16 {x}^{2} - 2x - 3 = 0[/tex]
[tex]a = 16[/tex]
[tex]b = - 2[/tex]
[tex]c = - 3[/tex]
[tex]\Delta= {b}^{2} - 4ac[/tex]
[tex]\Delta= {( - 2)}^{2} - 4 \times 16 \times ( - 3)[/tex]
[tex]\Delta=4 + 192[/tex]
[tex]\Delta= 196[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - ( - 2) \pm \sqrt{196} }{2 \times 16} = \frac{2 \pm14}{32} [/tex]
[tex]x_{1} = \frac{2 + 14}{32} = \frac{16}{32} = \frac{1}{2} \: \: verifica \: conditia[/tex]
[tex]x_{2} = \frac{2 - 14}{32} = - \frac{12}{32} = - \frac{3}{8} \: \: verifica \: conditia[/tex]
