Although the phrase "2-phase" is common, it's not actually true. In Canada and the USA the common household supply system runs three wires into the home from the transformer. Two of them are from opposite ends of the transformer secondary coil, and the third is from a center-tap of that coil. That last line is GROUNDED at the transformer and again in your house, establishing the 0 Volts reference point. It is called the NEUTRAL wire - it is NOT the same as the true GROUND wire that runs inside your house wiring. Referenced to that Neutral, each of the other two lines is at 110 VAC from it and are called "HOT" lines or L1 and L2. They actually are out of phase from each other by 180 degrees, so the difference between these two Lines (L1 to L2) is 220 VAC.
In Europe the wall outlet provides 220 VAC between the two power connection points (blades), and I do not know whether either of them is connected to Ground to establish a 0-volt reference point for the Neutral line. Here in North America the common household outlets provide 110 VAC between the two power connections (blades). Most commonly the WIDER of the two blades is the Neutral line - some older homes have outlets with both slots the same size. The Hot (narrower) blade is supplied from only ONE of the two Hot supply lines (L1 or L2) at the breaker panel.
In North America to provide 220 VAC to a load device you need to install special wiring. Well, in fact the wire cable in the wall may not be different (depends on current rating and on whether you need to supply the Neutral line at the outlet), but the outlet fitting AND the breaker supplying the circuit must be different. The outlet fitting must be unique so that no "regular" device (that uses 110 VAC) can be plugged in by mistake. Then of course, the plug on the end of the cord from your appliance (the computer in this case) must be installed to match the wall outlet configuration. The blade configuration is specified in Electrical Codes and depends both on the voltage and the maximum current rating (the breaker rating) of the circuit. The wire cable for the circuit also must match the maximum current of the breaker so that the breaker does provide adequate protection from over-current conditions causing excess heat.
The breaker is a particular type, called a dual-pole breaker. It draws power from both the L1 and L2 buses on the Breaker Panel to feed out to the circuit. It acts to sense current in BOTH of these two Hot lines and to switch BOTH of them off simultaneously. This ensures that there can be no voltage from either of the Hot lines out in the circuit wiring if the breaker is off.
So, to answer OP: you CANNOT feed your computer 220 VAC by fiddling with two 110 VAC standard house circuits. You must have a dedicated new circuit installed from the breaker panel with the correct breaker, wiring, and outlet fixture. Then you must change the plug on the end of your computer's cord and change its power supply input voltage setting switch if it has one.
You should NOT plug into a dryer outlet. That outlet has a breaker and wiring suitable for 220 VAC AND 35 to 40 Amps, to match a dryer's load. If you plug into that a device (your computer) wired with lighter wires for up to 15 amps, it could fail and draw 30 amps, sufficient to burn out its internal wiring and cause a fire, even though the breaker will NOT trip because it is not overloaded. The breaker is there to protect against overcurrent conditions in ALL of a circuit, including the house wiring AND the consumer device you plug into it. So the breaker and the consumer device's wiring need to be matched.
I guess you'll have to assess whether saving a couple percent in power supply efficiency is worth the time and expense of installing a new dedicated outlet for the computer. If you save 2% on a unit pulling big power like 1000 W, you'll save 20 watts. If the machine runs 24/7, that can come to about half a Kilowatt-Hour per day, or 175 KWH per year. Even if your electricity costs 15¢ per KWH, that gets to about $26 per year.
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