If `a`, `b`, `c` are real then `((a,b,c),(b,c,a),(c,a,b))=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)`

(a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)

(a+bomega+comega^(2))/(c+aomega+bomega^(2))

If a^3+b^3+6a b c=8c^3 & omega is a cube root of unity then: (a) a , b , c are in A.P. (b) a , b , c , are in H.P. (c) a+bomega-2comega^2=0 (d) a+bomega^2-2comega=0

Prove that a^3 + b^3 + c^3 – 3abc = (a + b + c) (a + bomega + comega^2) (a + bomega^2 + "c"omega) , where omega is an imaginary cube root of unity.

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in