How Did Viete Solve Roomen's Problem in 1595?

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In 1595, François Viète successfully solved Adriaan van Roomen's complex polynomial equation, which posed a significant challenge to mathematicians of the time. Viète's approach involved innovative techniques in algebra, particularly the use of symmetric functions and relationships between the roots. His work laid the groundwork for modern algebraic methods and contributed to the understanding of polynomial equations. The discussion highlights the importance of Viète's contributions and references various resources for further exploration of his methods. Overall, Viète's solution marked a pivotal moment in the history of mathematics.
Ethereal
In 1593, Adriaan van Roomen posed the following problem to "all the mathematicians of the known world": Find the roots of:

x^45 - 45x^43 + 945x^41 - 12300x^39 + 111150x^37 - 740459x^35 + 3764565x^33 - 14945040x^31 + 469557800x^29 - 117679100x^27 + 236030652x^25 - 378658800x^23 + 483841800x^21 - 488484125x^19 + 384942375x^17 - 232676280x^15 + 105306075x^13 - 34512074x^11 + 7811375x^9 - 1138500x^7 + 95634x^5 - 3795x^3 +45x = C

where C is a constant.

Viete solved this in 1595. How was this done?
 
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Better Link
http://francois-viete.wikiverse.org/
 
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Best link
explanation with mathmatics

http://pup.princeton.edu/books/maor/sidebar_d.pdf

sorry about having so many links
but i posted them as I found them
 
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