Solution:

Initial energy \(U_i = \frac{1}{2}CV_1^2 + \frac{1}{2}CV_2^2\). Common potential after connection \(V = \frac{CV_1 + CV_2}{C + C} = \frac{V_1 + V_2}{2}\) for like-polarity connection. Final energy \(U_f = \frac{1}{2}(2C)V^2 = C \left(\frac{V_1 + V_2}{2}\right)^2 = \frac{C}{4}(V_1^2 + V_2^2 + 2V_1V_2)\) . Decrease in energy \(Delta U = U_i - U_f = \frac{1}{4}C(V_1^2 + V_2^2 - 2V_1V_2) = \frac{1}{4}C(V_1 - V_2)^2\).