Op 01/03/2025 om 02:12 schreef Richard Hachel:
What if Descartes and Gauss were completely wrong?
No, not about everything, obviously, but about some important details?
What if there were two blunders hidden, correcting each other, according
to the theory of compensated errors?
First blunder: after having understood that the real roots were revealed
by x=[-b(+/-)sqrt(b²-4ac)]/2a, which is true and which is easily demonstrated, generalizing the same discriminant too quickly, without
paying attention to the signs (complexes being complex to handle) and
setting i²=-1 (which is true) then
x=[-b(+/-)i.sqrt(b²-4ac)]/2a instead of x=[-b(+/-)i.sqrt(b²+4ac)]/2a.
The complex root is no longer the same. There would therefore be a first error due to a misunderstood sign.
The error is then compensated by another sign error, during the proof by check via the reverse path. Thus, for me, the correct roots of
f(x)=x²-2x+8 are x'=4i, and x"=2i which can easily be placed on the
usual x'Ox axis of Cartesian coordinate systems, roots found elsewhere
by using x=[-b(+/-)i.sqrt(b²+4ac)]/2a without being trapped by a sign
error (we are no longer in real roots, but in complex roots, where x=-i
on the x'Ox axis and vice versa).
R.H.
If you think you have a superior theory of complex numbers, you're
better off making an engaging video on the subject and then you can
actually have some impact with potentially millions of views:
https://www.youtube.com/watch?v=5PcpBw5Hbwo
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