Algebra Simplification: Solving for X with Conjugates

[Axecutioner]

Problem:
[PLAIN]http://img40.imageshack.us/img40/1020/gahr.png
I need to simplify the x equation as far as I can, the y equation is x multiplied by it's conjugate, and the z equation is a failed attempt at further simplification. The last line is me checking which of the 3 (x, y, and z) equations are equal.

Basically, I need to take the y equation, keep not change the y at all, and get the other side simplified as much as I can.

Thanks!

 

[arildno]

Well, first off:
I don't see how "y" is a simplification of "x", or that the corrected "z" would simplify anything.

Stick instead with your "x" formula, and you may rewrite this, if not simplifying, as:
$$x=\frac{\sqrt{\frac{A}{B}}(\sqrt{\sin^{2}\theta-\frac{C\sqrt{B}}{\sqrt{A}}})+\sin\theta}{B}$$

This should also tell you where you went wrong in your "z"-expression.

 

[Axecutioner]

Thanks, that looks better. But uh...

Plug in the numbers I did in my x equation and you get 0.8164965809...
(2/3)^.5 = 0.8164965809...

So somehow my x equation simplifies to just (A/B)^.5

 

[arildno]

Well, it doesn't.

For example, with your "x"-expression, setting C=theta=0 makes x=0, rather than equal to the square root of A/B