How to deal with this equation involving a plus/minus term

[Dixanadu]

Hey guys,

So I'm reading a textbook which has the following equation:

\dot{X}^{-}\pm X^{-\prime}=\dfrac{1}{4\alpha' p^{+}}\left( \dot{X}^{I}\pm X^{I\prime} \right)^{2}.

Please note that the +,-,I are indices. Then the author says:

\dot{X}^{-}= \dfrac{1}{4\alpha' p^{+}}\left( \dot{X}^{I}\dot{X}_{I}+X^{I\prime}X_{I}^{'} \right)

where the repeated up and down index is using Einstein's summation convention.

I have no idea how you can get this equation from the first one...can someone explain please?

Thanks...

 

[robphy]

What happens if you write the first as two equations?
One with +, the other with -. Expand their right hand sides. Then add...