A sentence similar to your first one is described by Quirk* this way:
"In a formal and somewhat archaic usage, the subordinate clause in a such.....as construction is finite.....They were fed such sumptuous fare as kings dream of."
While a descriptive adjective, as in Quirk's sample sentence, often appears between "such" and its noun, ("such inspiring books", for example), it is not necessary.
Your first sentence is acceptable, though it sounds strained. This sentence could also be, more comfortably, "Let students read such books as those that will promote their motives for studying.
Your second sentence is formal, too, and it is acceptable.
The sentence could also be: "Let students read such inspiring books that they (the books) will promote their motives for studying." This modified construction is less formal.
The third kind of sentence is probably the most frequently used. It is neither formal nor informal.
The sentences all have the same meaning.
*A Comprehensive Grammar of the English Language, by Quirk, Greenbaum, Leech and Svartvik. Longman. 1985