MHT CET202313 May 2023Morning ShiftMathematicsSequences and SeriesActual
x, y, z are in G.P. and ⁻¹ x, ⁻¹ y, ⁻¹ z are in A.P., then
Options
- A6 x=4 y=3 z
- B2 x=3 y=6 z
- C6 x=3 y=2 z
- Dx=y=z
Correct answer
D. x=y=z
Step-by-step solution
x, y, z are in G.P. y^2=x z 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-x z = x+ z 1-x z aligned 2 y=x+ z x, y, z are in A.P. From (i) and (ii), we get x=y= Z