Derivation of relativity equation

[musicmar]

Homework Statement

Combine Eqs. 4.4 and 4.5 to derive Eq. 4.22

Homework Equations

4.4: p= m u/ (sqrt(1-(u²/c²)))
4.5: E= m c²/ (sqrt(1-(u²/c²)))
4.22: E²-(pc)²= (mc²)²

The Attempt at a Solution

(sqrt(1-(u²/c²))) = mu/p

(sqrt(1-(u²/c²))) = mc²/E

1 - u²/c² = m²u²/p²

1 - u²/c² = m²c⁴/E²

u²/c²=1-m²u²/p²

u²/c²=1-m²c⁴/E²

Now combining:

1 - m²u²/p² =
1 -m²c⁴/E²

m²u²E²=m²c⁴p⁴

Clearly, this is not Eq. 4.22 above. So, I either made a small mistake somewhere or missed a larger concept.

Thank you.

 

[zhermes]

Just a small mistake. You're not trying to solve these equations, so equating them isn't quite the right direction.

You're trying to show that E^2 - (pc)^2 = (mc^2)^2
Use your two other equations to solve for E^2, and (pc)^2; then subtract them. The right answer will pop out.