Lets call a the inverting input node, and b the non-inverting input
node.
In this problem, we shall call Va as the inverting input
node voltage and Vb as the non-inverting input node voltage, as V1
and V2 are already used.
We thus have Va = Vb
Question a.
At b, the KCL gives, as the current entering the op amp is zero:\
(V2 Vb)/R3 = Vb /R4
which gives
Moreover, we have V0 Va + Va V1 =
R2*io R1*io
V0 V1 = io*(R2 + R1)
So V0 = io*(R2 + R1) + V1
But from:
Va V1 = R1*io we can get i0 = V1/R1 Vb /R1
Then we get V0 = io*(R2 + R1) + V1
By substituting io above in this equation we get the result:
We need to solve
That corresponds to R2 = 11*R1 and also 1 + R2/R1 = 4*(1 + R3/R4),
which is 2*R4 = R2
All the different combinations that satisfy those two equations fit
here.