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`

If (b+c-2a)/a , (c+a-2b)/b , (a+b-2c)/c are in A.P. , then a,b,c are in :

If a, b, c are distinct real numbers such that a, b, c are in A.P. and a^2, b^2, c^2 are in H. P , then

If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a ,b ,a n dc are in A.P. (C). b=a+c (D). 3a=b+c

If omega is a cube root of unity, then find the value of the following: (a+bomega+comega^2)/(c+aomega+bomega^2)+(a+bomega+comega^2)/(b+comega+aomega^2)

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 are in A.P.

If a=z_1+z_2+z_3, b=z_1+omega z_2+omega^2z_3,c=z_1+omega^2z_2+omegaz_3(1,omega, omega^2 are cube roots of unity), then the value of z_2 in terms of a,b, and c is (A) (aomega^2+bomega+c)/3 (B) (aomega^2+bomega^2+c)/3 (C) (a+b+c)/3 (D) (a+bomega^2+comega)/3

If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. (d) a ,b ,c are in H.P.

If a^(2) , b^(2) , c^(2) are in A.P , pove that a/(a+c) , b/(c+a) , c/(a+b) are in A.P .