Solve the equation|x+a x x x x+a x x x x+a|=0,a≠0
Solution and Explanation
|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.
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