Question

if x,y,z are in AP show that (xy)^-1,(zx)^-1,(yz)^-1 are in AP

Answer 1

As given x, y, z are in AP.

Then, d ⇒ a₂ - a₁ = a₃ - a₂

And so,  y - x = z - y

Divide  xyz on both sides

          y - x / xyz = z - y / xyz

      y/xyz - x/xyz = z/xyz - y/xyz

         1/xz - 1/yz = 1/xy - 1/xz

Then, by converse of the d ⇒ a₂ - a₁ = a₃ - a₂

1/xy, 1/xz, 1/yz are in AP.

Hence (xy)^-1,(zx)^-1,(yz)^-1 are in AP.
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