Would it take 7 to 10 times more energy to lift a turbofan-helicopter?
Helicopter rotors are very large precisely for that reason. Lift from a rotor (or thrust from a propeller or fan) is obtained by accelerating a given mass of air m to a velocity v. The thrust obtained is proportional to the increase of momentum ∆mv. Obviously, you can get the same ∆mv by accelerating a given mass of gas to a high speed (propeller/fan) or by accelerating a larger mass to a lower speed (rotor). But the energy needed is proportional to v squared... Hence, and for the same thrust/lift, it's much more expensive, in energy or power terms, to use a propeller/fan than a big rotor ...