These new GE9x engines are huge and extremely powerful, but could two of them power a B747–8?
It is possible for some engines to power the original 741s but I am mainly interested in the B748.
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The curently operational GE90-115B engine is somewhat more powerful than the listed specs I've seen for the GE9X, at 115,540 lbf thrust vs just 105k.
That engine powers three current variants of the 777. Interesting to note that the 777-300ER is actually 5% heavier than the original 1966 version of the 747. Two of the 90-115 also have more takeoff thrust (~230k lbf) than the original 747-100 (~175-205k lbf).
So, in theory, two modern engines can power a 747, but only the original, not the 747-8.
Twins have higher thrust requirements, as they have to be able to take off with just one engine, while quads can use three. The 741's wings aren't as effective as the 777's, so even the 741's 5% lower weight might not quite suffice. But as the "741-twin" could use less fuel than the original, it could still maintain the 741's original payload and range.
There are other changes required for a twin and for ETOPS, so it won't be just a re-engine. All in all, a twin-powered aircraft with the early 747's fuselage, general layout and performance, but some control modifications, should be possible.
The 748 is a much heavier aircraft than the 741. It could in theory be ferried with the power of two GE9x engines, but its total weight would have to be restricted to less than that of a 741. That cuts its useful load in half - essentially, half the aircraft is now useless.
If operated, it wouldn't be able to fill all its seats or fly its full range. Such an aircraft would have no value for commercial operations. The only uses for it I can think of would be an oversized vomit comet or carrying something extremely light. And there are special aircraft with oversized fuselages for that like Airbus Beluga or Boeing Dreamlifter.
The minimum a modified 748 could operate commercially with is three modern engines. With two out of three GE9x running it would get 210,000 lbf of thrust, which is marginally above the 200k that three of the 748's engines produce.
TL;DR version: Two GE9x could keep a 748 in the air, but not in the black.
The 747-8 uses four GEnx-2B67B engines for a total maximum thrust of 296 x 4 = 1184kN. The GE9x is still under development but should provide 470kN. With two engines that amounts to 940kN, which is not nearly as much as the four engines of the 747 provide.
Would a 747-8 by able to fly with the power of two GE9x engines? In theory yes, but with less cargo capacity and a lower MTOW as the engines are less powerful. However in reality a 747 will never fly with two engines because the airframe and the wings are not designed for it.