threepointchargeseach‘q’isplacesatthethreeverticesofanequilatraltriange.findthemagnitudeandsignofthechargetobeplacedatthecentroidofthetriangeso thattheverticesareinequilibrium.

If we put positive charge at the centre, due to same polarity interaction, they will repel each other.
If negative, then due to attraction by three charge it would sustained its position.
Now, for the system to be in equilibrium, calculate the potential energy and double negative differential of the P.E. w.r.t. position must be zero.
Proceed in this way and calculate the energy.