Chapter 4, Problem 4.95IP

Bipolar Power Supply Voltages
The circuit in Figure P4-95 produces bipolar power supply voltages $V_{POS}>0$ and $V_{NEG}<0$ from a floating unipolar voltage source $V_{REF}>0.$ Note that the OP AMP output is grounded and that its $+V_{CC}$ and $-V_{CC}$ terminals are connected to $V_{POS}$ and $V_{NEG},$ respectively.

1. Show that $V_{POS}=+V_{REF}{/}^2$ and $V_{NEG}=-V_{REF}/2$ even if the load resistors $R_{POS}$ and $R_{NEG}$ are not equal.
2. If $R_{POS}$ and $R_{NEG}$ are not equal, a current $i_G$ must flow into or out of ground. How does the ungrounded voltage source $V_{REF}$ supply this ground current?
3. In effect, the OP AMP creates a "virtual ground" at point $A\left(V_A=0\right)$ but draws no current in doing so. Why not just connect point A to a "real ground" and do away with the OP AMP?