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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. )
josephus
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