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The red and white wires won't work on modern flat screen tvs.
Those red/white you see on back of the tv are inputs, not outputs.
Your rocker chair is only able to accept an analog input
the tv is only digital
If you look on back of the tv you should see a small square port with a little red light inside, that says Digital Audio Out
that is a digital fiber optic connection, and it is the only audio output a modern tv is capable of.
You would have to either buy a small converter box to adapt that digital output to the analog connection your chair uses, OR you could try connecting the chair directly to your source device (cable/satellite box, dvd, game console, etc), instead of trying to hook it to the tv.
I can recommend a converter box, if you'd like to try that route.