Yes, using Pythagorean Theorem, you get a total wind of 37 knots. But, if you break those up into vectors, you get a 17 knot tailwind and a 33 knot crosswind as the FMC shows.
The only wind affecting groundspeed will be the headwind or tailwind component of the total wind. In this case, 17 knots. To make sure I wasn't going crazy, I computed the winds both on a "regular" E6B and an electronic one. They both show a groundspeed of about 383 knots. That would make the FMC correct, a tailwind of 17 knots (GS minus TAS). But, the groundspeed on the ND shows 402 knots - when it should be about 383 based on E6B calculations.
You say, "the wind is pushing you sideways twice as much as it is forwards! You have to take the resultant wind vector to derive GS!"
Not quite, if you have a direct crosswind of 100 knots, your GS will not change by 100 knots. GS would be derived from the components of the total wind, not the total wind itself.
Anyway, this problem is not showing up in 3.50, so I will use that for now.
-Christian