Question

Am nevoie de ajutor la e1 ex a si c am nevoie urgent

Answer 1

$a) \sqrt{2x - 1} = 3$

Condiția de existență :

$2x - 1 \geqslant 0$

$\sqrt{2x - 1} = 3 \: | {( \: \: )}^{2}$

$2x - 1 = 9$

$2x = 9 + 1$

$2x = 10 \: | \div 2$

$x = 5 \: \: verifica \: conditia$

$c) \sqrt{2x + 3} = 4x$

Condiția de existență :

$2x + 3 \geqslant 0$

$\sqrt{2x + 3} = 4x \: | {( \: \: )}^{2}$

$2x + 3 = 16 {x}^{2}$

$16 {x}^{2} - 2x - 3 = 0$

$a = 16$

$b = - 2$

$c = - 3$

$\Delta= {b}^{2} - 4ac$

$\Delta= {( - 2)}^{2} - 4 \times 16 \times ( - 3)$

$\Delta=4 + 192$

$\Delta= 196$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - ( - 2) \pm \sqrt{196} }{2 \times 16} = \frac{2 \pm14}{32}$

$x_{1} = \frac{2 + 14}{32} = \frac{16}{32} = \frac{1}{2} \: \: verifica \: conditia$

$x_{2} = \frac{2 - 14}{32} = - \frac{12}{32} = - \frac{3}{8} \: \: verifica \: conditia$