Buring hydrogen means we need to get hydrogen. Mostly from methane or water. To do this we use electricity to break the hydrogen free and collect it. If we then burn it, we get water as the result. So if our source of hydrogen is water, it takes just as much energy to make the hydrogen as we get out of it by burning it.
If we fuse the hydrogen together, we get helium, and that reaction releases a lot more energy than burning hydrogen, so we end up with a net gain of energy.
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