Solve : `|[x,c+x,b+x],[c+x,x,a+x],[b+x,a+x,x]|=0`

Solve for x: |[x,c+x,b+x],[c+x,x,a+x],[b+x,a+x,x]|=0

Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

a+b+c=0, solve for x : [[a-x,c,b],[c,b-x,a],[b,a,c-x]]=0

If a+b+c=0, solve the equation: |[a-x, c, b],[c,b-x, a],[b, a, c-x]|=0

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

Solve the following determinant equation: |[x+a, b, c], [c, x+b, a], [a ,b, x+c]|=0

If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.