Learn English – the word that best describes this

An applicable neologism is humblebrag, a boast couched in self-deprecation. Henry Alford describes it as the false modesty of a plea intended to be met with both awe and sympathy. Humblebrag is attributed to Harris Wittels, a writer for the NBC sitcom Parks and Recreation who Tweets celebrity examples at that handle and has collected them into a book.

A less popular term from a different U.S. sitcom is backdoor brag, from a 2008 episode of 30 Rock. While not as buzzworthy a term, the example used in the episode matches one of yours:

It’s sneaking something wonderful about yourself into everyday conversation… Like when I tell people it’s hard for me to watch American Idol, because I have perfect pitch.”

Update: J.P. Freire in the American Spectator (a politically conservative U.S. magazine) proposes whinebrag, photobrag, busybrag, sorrybrag, and emobrag to capture additional flavors of show-offy self-deprecation. Who knows if any of them will gain currency; he notes the overlap of whinebrag with first-world problems a.k.a. white whines, and the Harvard Business Review lamented the busybrag months ago.

You seem to have two different kinds of examples there. In the first example the solution set is ill-defined:

A set is well-defined if any given object either is an element of the set, or is not an element of the set

but it's never clear whether a given number a is an element of the solution set to the equation; whether it is or not depends (as you state) on the value of b.

In your second example, the solution set (that is, the set of solutions to the problem posed) is well-defined, but empty because the conditions are impracticable:

(Definition 2) not practicable : incapable of being performed or accomplished by the means employed or at command