Question

. Помогите пожалуйста с решением​

Answer 1

Ответ:

$2\cdot \Big|\, |x|-4\, \Big|-6=0\ \ \Rightarrow \ \ \ 2\cdot \Big|\, |x|-4\, \Big|=6\ \ \ ,\ \ \ \Big|\, |x|-4\, \Big|=3\ \ \Rightarrow \\\\|x|-4=\pm 3\\\\a)\ \ |x|-4=-3\ \ ,\ \ |x|=-3+4\ \ ,\ \ |x|=1\ \ ,\ \ x=\pm 1\\\\b)\ \ |x|-4=3\ \ ,\ \ \ |x|=3+4\ \ ,\ \ |x|=7\ \ ,\ \ \ x=\pm 7\\\\Otvet:\ \ x_1^2+x_2^2+x_3^2+x_4^2=1^2+(-1)^2+7^2+(-7)^2=98\ .$

$\star \ \ |x|\geq 0\ \ ,\ \ |x|=\left\{\begin{array}{l}x\ ,\ esli\ x\geq 0\ ,\\-x\ ,\ esli\ x<0\ .\end{array}\right\ \ \star$