If x, y, z are in Arithmetic Progression and ⁻¹ x, ⁻¹ y, ⁻¹ z are also in Arithmetic progression, where x, z 0 and x z 1, y 1 , then

Step-by-step solution

Given, x, y, z are in A.P. 2 y=x+z...(i) Also, ⁻¹ x, ⁻¹ y, ⁻¹ z are in A.P. aligned & 2 ⁻¹ y= ⁻¹ x+ ⁻¹ z & ⁻¹ ( 2 y 1-y^2 )= ⁻¹ ( x+z 1-x z ) & 2 y 1-y^2 = x+z 1-x z & 2 y 1-y^2 = 2 y 1-x z ...[From(i)] & 1-y^2=1-x z & y^2=x z aligned x, y, z are in G.P...(ii) From (i) and (ii), we get x=y= z x=y= z