Question

Произведение корней уравнения равно решите подробно,

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

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