Question

Найдите сумму корней уравнения x^2-6|x|-7=0

Answer 1

$x^2-6|x|-7=0$
$(|x|)^2-6|x|-7=0$
замена $|x|=t geq 0$
$t^2-6t-7=0,and,t geq 0$
$t^2+t-7t-7=0,and,t geq 0$
$t*t+t*1+(-7)*t+(-7)*1=0,and,t geq 0$
$t*(t+1)+(-7)*(t+1)=0,and,t geq 0$
$[t+(-7)]*(t+1)=0,and,t geq 0$
$(t-7)(t+1)=0,and,t geq 0$
$[t-7=0,or,t+1=0],and,t geq 0$
$[t=7,or,t=-1],and,t geq 0$
$t=7$
$|x|=7$
$x=pm7$

$sum=7+(-7)=0$

Ответ: $0$