If a+b+c=0, then the solution of the equation a-xcbcb-xabac-x=0 is

a−xcbcb−xabac−x=0⇒a+b+c−xcba+b+c−xb−xaa+b+c−xac−x=0⇒(Σa−x)1cb1b−xa1ac−x=0⇒x=Σa=0(b−x)(c−x)−a2−cc−x−a}t+b{a−b+x}=0or  x2−a2+b2+c2+(ab+bc+ca)=0x2−Σa2+Σab=0x2−Σa2−12Σa2=0∵a+b+c=0⇒(a+b+c)2=0⇒Σa2+2Σab=0⇒Σab=−12Σa2Or  x=±32Σa2The solution  is x=0  or  ±32Σa2