Grandma's got a Sony Bravia KDL-40L4000 flatscreen TV. For Christmas, we bought her a Logitech X-530 speaker system so she could hear better.

Now, her TV only has stereo output with 2 RCA jacks (red-white). When I plug them into the speakers, only the two front satellites, the center one, and the subwoofer output sound. The back satellites don't play nothing but tiny noises, like filtered by the speaker system. The TV has no 5.1 output, only 2.0.
I'd like to know if I can build some kind of adapter that would
- send left channel from the TV to the front left + back left speakers
- send right channel from the TV to the front right + back right speakers
- average left+right channels from the TV to the center speaker and to the subwoofer.
Could that be achieved with just a few diodes and RCA jacks?
Like that :
TV LEFT ------>|------\------>|---- FRONT LEFT
\----->|---- REAR LEFT
(>)--->|---- CENTER+SUB
/----->|---- REAR RIGHT
TV RIGHT ------>|------/------>|---- FRONT RIGHT
What to put at the (>) "joining point" ? How to wire the grounds?