If a, b, c are in A.P, show that` (i)a^3+b^3+6abc=8b^3` (ii) `(a+2b-c)(2b+c-a)(a+c-b) =4abc`

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c are in A.P.

If a+ b + c = 0 , show that : a^(3) + b^(3) + c^(3)= 3abc

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a,b,c are in A.P., then a^(3)+c^(3)-8b^(3) is equal to

If a, b and c are in A.P. show that : (i) 4a, 4b and 4c are in A.P. (ii) a + 4, b + 4 and c + 4 are in A.P.

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .