You just want to multiply by N preserving the dc component.
So drop the cap on input, that drops th dc component you want to keep. Then for your non-inverting inputs, you don't want to DC bias them up with your resistor divider, since the DC bias comes from your signal., send them to ground like normal. so you are multiplying by -sqrt(N) * -sqrt(N) = N.
You can also probably do it as a single non-inverting op amp, and if you have a op amp that can go to ground on input and output you won't even need to supply a negative voltage.