a^2+1/4b^2+5=4a+b-|c-2│
a²-4a+1/4b²-b+5+│c-2│=0
a²-4a+4+1/4b²-b+1+│c-2│=0
(a-2)²+(1/2b-1)²+│c-2│=0
∴a-2=0 1/2b-1=0 c-2=0
a=2 b=2 c=2
∴△ABC是等边三角形