Question

Ркшите (х-2)/\2 - 8|х-2|+15=0

Answer 1

Ответ:

$(x - 2 {)}^{2} - 8 |x - 2| + 15 = 0 \\ |x - 2| = \sqrt{(x - 2 {)}^{2} }$

$(x - 2 {)}^{2} - 8 \sqrt{(x - 2)^{2} } + 15 = 0 \\ \sqrt{(x - 2 {)}^{2} } = t \\ {t}^{2} - 8t + 15 = 0 \\ t_{1} =3 ;t _{2} = 5 \\ |x - 2| = 3 ;|x - 2| = 5 \\ x - 2 = 3 \iff \: x = 5 \\ x - 2 = - 3 \iff \: x = - 1\\ x - 2 = 5 \iff \: x = 7\\ x - 2 = - 5 \iff \: x = - 3$

ответ: х=-3; -1; 5; 7;