Question

|x-8|=0
|x+18|=0
|x-3|+|x la puterea 2 -9|=

Va rog ,macar primele doua.

Answer 1

$\star) |x - 8| = 0$

$1)x - 8 = 0$

$x = 8$

$2) - x + 8 = 0$

$- x = - 8 \: | \times ( - 1)$

$x = 8$

$\star) |x + 18| = 0$

$1)x + 18 = 0$

$x = - 18$

$2) - x - 18 = 0$

$- x = 18 \: | \times ( - 1)$

$x = - 18$

$\star) |x - 3| + | {x}^{2} - 9| = 0$

$1)x - 3 + {x}^{2} - 9 = 0$

$x - 3 + (x - 3)(x + 3) = 0$

$(x - 3)(1 + x + 3) = 0$

$(x - 3)(x + 4) = 0$

$= > x - 3 = 0 = > x = 3$

$= > x + 4 = 0 = > x = - 4$

$2) - x + 3 - {x}^{2} + 9 = 0$

$- {x}^{2} - x + 12 = 0 \: | \times ( - 1)$

${x}^{2} + x - 12 = 0$

$a = 1$

$b = 1$

$c = - 12$

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

$\Delta = {1}^{2} - 4 \times 1 \times ( - 12)$

$\Delta = 1 + 48$

$\Delta = 49$

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

$x_{1,2}=\frac{-1\pm\sqrt{49}}{2 \times 1}$

$x_{1,2}=\frac{-1\pm7}{2}$

$x_{1}=\frac{-1 + 7}{2}$

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

$x_{1}=3$

$x_{2}=\frac{-1 - 7}{2}$

$x_{2}= - \frac{8}{2}$

$x_{2}= - 4$