Although the question shows considerable effort to achieve clarity, the way it is phrased as:
How many molecules of nucleoside triphosphate… [does] it take to release enough energy
still allows ambiguity, as I would not really regard the NTPs involved in protein synthesis “releasing energy”. So let us consider two reformulations of the question, as the explanation of the answers is of more scientific interest than the actual answers.
1. How many molecules of NTP are hydrolysed in the reactions causing the formation of one peptide bond on the ribosome?
Answer = 3
Formation of each peptide bond involves a cycle consisting of the introduction of a single new aminoacyl-tRNA to the A site of a ribosome carrying a growing polypeptide chain (or initiator tRNA for the first peptide bond), the peptidyl transferase reaction, and than translocation of the extended peptidyl-tRNA from A- to P-site. (See, e.g. Berg et al. online — Ch. 29)
1 ATP is hydrolysed in the aminoacylation reaction:
Amino Acid + tRNA + ATP → Aminoacyl-tRNA + AMP + PPi
1 GTP is hydrolysed in the aatRNA binding reaction catalysed by EF-Tu/EF1.
1 GTP is hydrolysed in the translocation reaction catalysed by EF-G/EF2
No NTP is consumed directly in the peptidyl transferase reaction — the energy for bond formation comes from the ‘activated’ aminoacyl-tRNA.
2. What is the total energetic cost in molecules of ATP for the formation of one peptide bond?
Here one might argue that:
Answer = 4+
The additional ATP occurs if one considers the total energetic cost of the aminoacylation reaction as 2 ATP, not 1 ATP. This arises from the fact that the ATP is hydrolysed to AMP (+PPi) and not ADP. Recycling of the AMP involves first the use of 1 molecule of ATP in the adenylate kinase reaction to produce ADP:
ATP + AMP ⇄ 2ADP
followed by the energy (from membrane ATP synthase) to regenerate ATP from ADP:
ADP + Pi ⇾ ATP
Why 4+? Certain amino acids (e.g. val and ile) are sufficiently similar to one another that the aminoacyl-tRNA synthetases have evolved a proof reading capacity, in which any incorrectly aminoacylated tRNA is hydrolysed. This only occurs for certain amino acids and at a rate that is difficult to determine, so the wastage of the ATP in this manner cannot be calculated precisely.