The trio were identified as J Mahesh, B Naveen and B Shiva, police said, adding a hunt is on to nab two others who are absconding.
All of them were friends, they said.
Police said the five conspired to kill the student Sudheer after he, his brother and some friends assaulted three of them over a period of time over a issue on March 9.
Sudheer was allegedly chased and hacked to death while he was on his way to write exams yesterday at around 8.30 AM.
Sudheer got off his two-wheeler when he was attacked and boarded a bus, but the gang pulled him out and hacked him to death on the roadside, Assistant Commissioner of Police (Kukatpally Division) N Bujanga Rao had said.