Question

Resolva a equação |x - 6|² - 17|x - 6| + 60 e assinale a alternativa que contém seu conjunto verdade, em U = R:

Answer 1

$\displaystyle \sf |x-6|^2-17|x-6|+60=0 \\\\ \underline{Fa{\c c}amos }: \\\\ |x-6|= a \\\\ \underline{Da{\'i}}} : \\\\ a^2-17a+60=0 \\\\ a = \frac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot 1} \\\\\\ a = \frac{17\pm\sqrt{289-240}}{2} \to a = \frac{17\pm\sqrt{49}}{2} \\\\\\ a =\frac{17\pm7}{2} \\\\ a = \frac{17+7}{2}\to a = 12 \\\\\\ a = \frac{17-7}{2}\to a = 5$

Daí :

$\sf 1^\circ \ \\\\ |x-6| = 12 \\\\ x - 6 = 12 \to \boxed{\sf x = 18 }\\\\ ou \\\\ x-6 = -12 \\\\ \boxed{\sf x = -6 }$

$\sf 2^\circ\\\\ |x-6| = 5 \\\\ x - 6 = 5 \to \boxed{\sf x = 11 }\\\\ ou \\\\ x-6 = -5 \to \boxed{\sf x = 1 }$

Portanto :

$\huge\boxed{\sf S = \{1,11,-6,18 \} }\checkmark$