Hello, I kind of just need a check for this question...

a)Given 3 currents, I1, I2, I3, and 3 resistors R1, R2, R3, minimize the energy

E=I1^{2}R1 + I2^{2}R2 + I3^{2}R3, with constraint G(I1,I2,I3) = I1+I2+I3=I, a constant.

b)Then it asks show that the ration of currents to resistance satisfy

I1:I2:I3=R2R3:R3R1:R1R2

I started with L(I1,I2,I3,lamda), then differentiated wrt all of the variables and set the equations =0. Then I solved for lamda then found that I1R1=I2R2=I3R3. Is this correct? If so how can I then solve for the minimum energy???

Then as for part b) I ended up finding that I1=C*R2R3, I2=C*R3R1 and I3=C*R1R2, C being a constant I/(R2R3+R1R3+R1R2).

Is this answer then sufficient for the last part of the question?

Any help is really appreciated.