If `a^(1//x) =b^(1//y) =c^(1//z)` and a,b,c are in G.P . Then :

If a^x=b^y=c^z and a, b, c are in G.P. then x,y,z are in :

If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,c are in A.P.

If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P, prove that a, b, c are in A.P.

If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(a+c) and b/d=(3a-c)/(a+c) .

If 1/(a+b)+1/(b+c)=1/b , prove that a, b, c are in G.P.

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then

If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c^(2)+d^(2) are also in G.P.

If a, b and c are any three vectors and their inverse are a^(-1), b^(-1) and c^(-1) and [a b c]ne0 , then [a^(-1) b^(-1) c^(-1)] will be

If a ((1)/(b) + (1)/(c)) , b((1)/(c) + (1)/(a)) , c ((1)/(a)+ (1)/(b)) are in AP then a, b, c are in :

If a,b,c are in A.P. and a^2,b^2,c^2 are in H.P. then which of the following could and true (A) -a/2, b, c are in G.P. (B) a=b=c (C) a^3,b^3,c^3 are in G.P. (D) none of these