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## Homework Statement

If a,b,c, are at the same time fifth, seventh and thirty seventh member of arithmetic and geometric progression then [itex]a^{b-c}b^{c-a}c^{a-b}[/itex] is:

## The Attempt at a Solution

I tried solving system of equations but i have four unknown. I was able to reduce it to on unknown.

12r^32 - 32r^12 + 20=0 where r is common ration in geometric series. I have no idea how to solve this.

Maybe trying to solve the system isn't a way to go?