Question

The effective resistance between A and B

Answer 1

2 +2+2=6ohm

(1/6+1/3)^-1

=2 ohm

this repeated again
hence answer is 6 ohm

Answer 2

Let total resistance be x then we can say that overall resistance will not get affected if we remove a loop of resistance (two 2 ohms resistance in series and one 3 ohms in parallel) then we can make an equation

x=2+3x/3+x

3x+x²=6+2x +3x

3x+x²=6+5x

x²-2x-6=0

After solving

[x=2±√4-4(-6)(1)]/2

x=(2±√28)/2

x=(2+√28)/2

the other one is eliminated as the value of resistance becomes negative