Question

Solve the equation|x+a x x x x+a x x x x+a|=0,a≠0

Answer 1

|x+a x x x x+a x x x x+a|=0
Applying R1->R1+R2+R3,we get:
|3x+a 3x+a 3x+a x x+a x x x x+a|=0
⇒(3x+a)|111 x x+a x x x x+a|=0

Applying C2->C2-C1 and C3->C3-C1,we have:
(3x+a)|100 xa0 x0a|=0

Expanding along R1,we have:
(3x+a)[1xa2]=0
⇒a2(3x+a)=0
But a≠0,
Therefore we have
3x+a=0
⇒x=-a/3.