Thread: Help me resolve this...

I have this equation that I would like to simplify.





I suspect that the equation is actually independent of r.

But I am having a hard time simplifying so that it is only expressed in terms of c and d.

Can you guys help me out?

That's NOT an equation, so nothing can be done...

Let's make it equal to K. Here's the quadratic you'd get:

r^2[c^2(16d^2 - 16K - 4c^2)] + r[c^3(16d^2 - 16K - 4c^2)]
+ c^2(8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2) = 0

You could let U = 16d^2 - 16K - 4c^2, so getting a more manageable:

r^2(Uc^2) + r(Uc^3) + c^2(8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2) = 0

I guess you could now let V = 8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2, to get:

r^2(Uc^2) + r(Uc^3) + Vc^2 = 0

r = [-Uc^3 +- SQRT(U^2 c^6 - 4UVc^4)] / (2Uc^2)

WHERE d'heck did you ever get that anyway?