If x, y, z are in GP, then which of the following is/are correct? 1. (3 x), (3 y), (3 z) are in AP 2. x y z+ (), x y z+ (y), x y z+ (z) are in HP Select the correct answer using the code given below.

Step-by-step solution

Since, x, y and z are in G.P y^2=x z Taking at base e both sides (y^2 )= (x z) 2 (y)= (x)+ (z) ....(i) aligned & (x), (y) and (z) are in A.P. & adding x y z & So, x y z+ (x), x y z+ (y), x y z+ (z) are also in A.P. & Now, (3 x)+ (3 z)= (3)+ (x)+ (3)+ (z) & =2 (3)+ (x)+ (z) aligned =2 (3)+2 (y) [ from ( i )] aligned & =2 (3 y) & (3 x), (3 y) and (3 z) are in A.P. aligned