A current of 20 amperes branches into currents x, y, and z through resistors with resistences 3, 7, and 5 ohms as shown. I=x, R=3 I=y, R=7 I=20 amps I=z, R=5 It is known that the current splits in such a way that the sum of the currents through the three resistors equals the initial current. The energy generated in each resistor is given by E = I2R, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and z which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) x = y = amps amps Z = amps