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:

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

Please note that the [itex]+,-,I[/itex] are indices. Then the author says:

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

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...