how can we solve a linear equation of this type

[aditi5000]

given r = 2^ (8/9) - 2^(1/9)

solve the following equation for p2/p1 or p1/p2
(p2/p1) ^ (-1/9) + 2 + r(p1/p2) - (p1/p2)^(8/9) = 2+r

answer is given as 2,1/2 and 1.

I am only getting 2 and 1. Please help...

This is a question under general equilibrium from chapter 15 (Andreu Mas-Colell, Michael Whinston, and Jerry Green - Microeconomic Th.)

[aditi5000]

Someone please help out on this one... Thank you!

[Chinni18]

Hi Aditi. I too am not getting 1/2 as a root. Even 1 came out to be a solution only after a lot of manipulation. Couldn't figure it out.

[aditi5000]

Hey Chinni, thanks for trying! :)