What happens when I use two outputs on a single speaker?

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If you take two identical 50W amps (each designed for 8 ohm speakers), parallel them and connect to an 8 ohm speaker then you will get 50W. If you are lucky the amps will not be damaged. If you are unlucky (i.e. the amps are not identical) then one or both amps may be damaged. In general, not a sensible thing to do.

You could connect them via ballast resistors, and then you get something like an amp which can deliver maybe 80-90W into 4 ohms.
 
Paralleling serves to increase current capability into lower impedance loads but requires well matched gains and impedance to share the load. If things are not well matched then one amplifier can source or sink current from the other. Due to most amplifiers using feedback, which means low output impedance, the two amplifiers can basically 'fight' to the death.

If the speakers are 8 ohm and the amplifiers are 4 ohm capable, then bridging is the way to higher power. This requires one amp be fed the same signal as the first, but inverted. The math says power goes up by a factor of four, reality will be less than this, often quite a bit less.
 
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