Help with Energy at inelastic collision

[FLms]

Homework Statement

A particle of mass m₁ and momentum p₁ collides with a particle of mass m₂ at rest. A reaction occurs, as a result giving two new particles, with masses m₃ and m₄, that are emitted at angles
$\theta_3$ and $\theta_4$, in relation to the original direction of m₁. Determine the energy Q that has been produced on the reaction in terms of the masses, the angles and p₁.

Homework Equations

$$Q = T_f - T_i$$
$$T = \frac{p^2}{2 m}$$

The Attempt at a Solution

$$p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)$$
$$p_2 = 0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)$$
$$Q = T_3 + T_4 - T_1$$
$$Q = \frac{{p_3}^2}{2m_3} + \frac{{p_4}^2}{2m_4} - \frac{{p_1}^2}{2m_1}$$

I'm stuck here.
I suppose I have to, obviously, express both $p_3$ and $p_4$ in terms of $p_1$, but I'm not exactly sure of how to do it. Or maybe I just need some algebraic manipulation to get rid of both $p_3$ and $p_4$.

Any help appreciated.

 

[ojs]

That absolutely correct, you need algebraic manipulation to express $p_3$ and $p_4$ in terms of $p_1$, $\theta_3$ and $\theta_4$.

 

[Redbelly98]

... and these are the equations you need to manipulate:

$$p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)$$
$$0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)$$