Proof of KE loss in inelastic collision

[Xizel]

Homework Statement

Prove that a perfectly inelastic collision loses more kinetic energy than a partially inelastic collision. Given: $$m_1, m_2, v_{1i}, v_{2i}, v_{1f}, v_{2f}$$

Homework Equations

$$KE = \frac{1}{2}mv^2$$

The Attempt at a Solution

From conservation of momentum:
$$P_{inelastic} : m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$$
$$P_{partial} : m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$$

I'm not sure how to progress from this. Thanks.

 

[Simon Bridge]

Compare energy before collision with energy after collision for each case.