Special Relativity, equation help needed

[punkstart]

Given that E² = c²p² + m_o²c⁴-----------(1);
where p represents the relativistic momentum p=\gammam_ou,
show that m=(p²c²-T²)/(2Tc²) where m is the relativistic mass of the particle,and T it's kinetic energy.

Homework Equations

E= T+m_oc²-------(2)

The Attempt at a Solution

I start by saying p²c²= E²-m_o²c⁴ (from (1)), subtracting T² from both sides gives
p²c² -T² = E²-m_o²c⁴-T² . Now using (2) i expand E;

p²c² -T²= (T+m_oc²)²-m_o²c⁴ -T² which gives
p²c² -T²= T²+2Tm_oc²+m_o²c⁴ -m_o²c⁴ -T²; simplifying

p²c² -T² = 2Tm_oc² Now dividing by 2Tc² gives

(p²c²-T²)/(2Tc²) = (2Tm_oc²)/(2Tc²) I now have the required LHS of (1),

This yields (p²c²-T²)/(2Tc²) = m_o , NOT m !

Where have i gone wrong !??

 

[vela]

Your work looks fine to me. The problem appears to be wrong.