Question

Îmi trebuie urgent !
ex: 6 doar : a , b ,c ,e , g !
vă rog !

Answer 1

$a)(x + 2)(x - 5) = 0$

$= > x + 2 = 0 = > x_{1} = - 2$

$= > x - 5 = 0 = > x_{2} = 5$

$b) {x}^{2} - 4 = 0$

${x}^{2} = 4$

$x = \pm \sqrt{4}$

$x = \pm2$

$= > x_{1} = 2$

$= > x_{2} = - 2$

$c) {(x + 2)}^{2} = 5(x + 2)$

${x}^{2} + 4x + 4 = 5x + 10$

${x}^{2} + 4x - 5x + 4 - 10 = 0$

${x}^{2} - x - 6 = 0$

$a = 1$

$b = - 1$

$c = - 6$

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

$\Delta = {( - 1)}^{2} - 4 \times 1 \times ( - 6)$

$\Delta = 1 + 24$

$\Delta = 25>0=>\exists\:x_{1}\:\neq\:x_{2}\:\epsilon\: \mathbb{R}$

$x_{1,2} = \frac{ - b \pm \sqrt{\Delta} }{2a}$

$x_{1,2} = \frac{ - ( - 1) \pm \sqrt{25} }{2 \times 1}$

$x_{1,2} = \frac{1 \pm5}{2}$

$x_{1} = \frac{1 + 5}{2} = \frac{6}{2} = 3$

$x_{2} = \frac{1 - 5}{2} = \frac{ - 4}{2} = - \frac{4}{2} = - 2$

$e) {x}^{2} - 3x = 0$

$a = 1$

$b = - 3$

$c = 0$

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

$\Delta = {( - 3)}^{2} - 4 \times 1 \times 0$

$\Delta = 9>0=>\exists\:x_{1}\:\neq\:x_{2}\:\epsilon\: \mathbb{Q}$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$

$x_{1,2}= \frac{ - ( - 3) \pm \sqrt{9} }{2 \times 1}$

$x_{1,2}=\frac{3\pm3}{2}$

$x_{1}=\frac{3 + 3}{2} = \frac{6}{2} = 3$

$x_{2}=\frac{3 - 3}{2} = \frac{0}{2} = 0$

$g)2 {x}^{2} - 1 = 3 {x}^{2} + 1$

$2 {x}^{2} - 3 {x}^{2} = 1 + 1$

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

${x}^{2} = - 2$

$x = \pm \sqrt{ - 2} = > nu \: exista$