Question

Произведение корней уравнения равно $x^2-12=|x|$
Решите подробно, пожалуйста

Answer 1

$x^2-|x|-12=0 \ |x|^2-|x|-12=0 \ left { {{t^2-t-12=0} atop {|x|=t geq 0}} right. \ left { {{t^2+3t-4t-12=0} atop {|x|=t geq 0}} right. \ left { {{t(t+3)-4(t+3)=0} atop {|x|=t geq 0}} right. \ left { {{(t-4)(t+3)=0} atop {|x|=t geq 0}} right.\ left { {{t=4 or t = -3} atop {|x|=t geq 0}} right. \ left { {{t=4} atop {|x|=t geq 0}} right. \ |x|=4\ x=-4 or 4$

Ответ: $4*(-4)=16$

Достаточно подробно?

Answer 2

$mathtt{x^2-12=|x|;~x^2-|x|-12=0;~(|x|+3)(|x|-4)=0;~|x|-4=0;~}\mathtt{|x|=4,~x=б4;~x_1x_2=-4*4=-16}$