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

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[latex]x^2-6|x|-7=0[/latex] [latex](|x|)^2-6|x|-7=0[/latex] замена [latex]|x|=t \geq 0[/latex] [latex]t^2-6t-7=0,and,t \geq 0[/latex] [latex]t^2+t-7t-7=0,and,t \geq 0[/latex] [latex]t*t+t*1+(-7)*t+(-7)*1=0,and,t \geq 0[/latex] [latex]t*(t+1)+(-7)*(t+1)=0,and,t \geq 0[/latex] [latex][t+(-7)]*(t+1)=0,and,t \geq 0[/latex] [latex](t-7)(t+1)=0,and,t \geq 0[/latex] [latex][t-7=0,or,t+1=0],and,t \geq 0[/latex] [latex][t=7,or,t=-1],and,t \geq 0[/latex] [latex]t=7[/latex] [latex]|x|=7[/latex] [latex]x=\pm7[/latex] [latex]sum=7+(-7)=0[/latex] Ответ: [latex]0[/latex]