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Topic: a problem about cubic equations
Replies: 4   Last Post: Nov 1, 2011 9:32 PM

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Posts: 54
Registered: 12/13/04
a problem about cubic equations
Posted: Oct 28, 2011 10:37 PM
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I keep seeing X^3- 2AX^3 + APX - 2A^2P =0

it appears in the derivation of relativistic equations.

it is asserted to have 3 REAL solutions. No Problem. until I
tried to divide the equation with X-2A

F(X) = (X-2A)(X^2 + AP)

this equation has 1 REAL root and 2 imaginary roots.

however that means it does not support the relativistic
equations asserted on its relationship. I have seen the same equation
in several places. usually they mangle the constant term. but the
shape of the equation does not change it would have 1 real and 2
imaginary solutions. it is asserted as having 3 REAL roots.

Is this a kind of mathematical religion? that this
particular equation would have 3 real roots?


for your pleasure

Consider the following

R^3 * H * Tan(A")^3/T^2 = (A+B)

H is 188098.0536 and is a conversion constant
R is in parsecs
A is in arc seconds
T is in years
(A+B) is in solar masses

the equation is complete. it can be freely rearranged to
solve for any missing term R, T ,(A+B) or even A" and H can be
recovered too. it is applied to double stars and orbiting units. it is
useful because not every set of orbits is rational.

( I published the derivation some years ago. )


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