If `|[x+a,a^2,a^3],[x+b,b^2,b^3],[x+c,c^2,c^3]|=0` and `a ne b ne c` then find the value of `x`.

If a^(2)+ab+b^(2) = b^(2) +bc +c^(2) where a ne b ne c then find the value of a+b+c .

FInd x when det[[x+a,a^(2),a^(3)x+b,b^(2),b^(3)x+c,c^(2),c^(3)]]=0 where a,b,c are distinct numbers and a!=b!=c

If a+b+c=0 , then find the value of (x^(a))^(3)/(x^(-3b)x^(-3c))

If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B , then find the value of det. (A^(3)+B^(3)+C^(3)) .