\( \newcommand{\abcp}[3]{\frc{#1+\sqrt{#2}}{#3}} \newcommand{\chao}[1]{\left\lfloor #1 \right\rfloor } \newcommand{\nPr}[2]{{}^{#1}A_{#2} } \newcommand{\combin}[2]{{}^{#1}C_{#2} } \newcommand{\cmod}[3]{#1 \equiv #2\left(\bmod {}{#3}\right)} \newcommand{\frc}[2]{\displaystyle\frac{#1}{#2}} \newcommand{\mdc}[2]{\left( {#1},{#2}\right)} \newcommand{\mmc}[2]{\left[ {#1},{#2}\right]} \newcommand{\cis}{\mathop{\rm cis}} \newcommand{\ImP}{\mathop{\rm Im}} \newcommand{\ReP}{\mathop{\rm Re}} \newcommand{\sen}{\mathop{\rm sen}} \newcommand{\tg}{\mathop{\rm tg}} \newcommand{\cotg}{\mathop{\rm cotg}} \newcommand{\cosec}{\mathop{\rm cosec}} \newcommand{\cotgh}{\mathop{\rm cotgh}} \newcommand{\cosech}{\mathop{\rm cosech}} \newcommand{\sech}{\mathop{\rm sech}} \newcommand{\sh}{\mathop{\rm sh}} \newcommand{\ch}{\mathop{\rm ch}} \newcommand{\th}{\mathop{\rm th}} \newcommand{\senEL}[1]{\mathop{\rm sen}^{#1}} \newcommand{\tgEL}[1]{\mathop{\rm tg}^{#1}} \newcommand{\cotgEL}[1]{\mathop{\rm cotg}^{#1}} \newcommand{\cosecEL}[1]{\mathop{\rm cosec}^{#1}} \newcommand{\shEL}[1]{\mathop{\rm sh^{#1}}} \newcommand{\chEL}[1]{\mathop{\rm ch^{#1}}} \newcommand{\thEL}[1]{\mathop{\rm th^{#1}}} \newcommand{\cotghEL}[1]{\mathop{\rm cotgh^{#1}}} \newcommand{\cosechEL}[1]{\mathop{\rm cosech^{#1}}} \newcommand{\sechEL}[1]{\mathop{\rm sech^{#1}}} \newcommand{\senq}{\senEL{2}} \newcommand{\tgq}{\tgEL{2}} \newcommand{\cotgq}{\cotgEL{2}} \newcommand{\cosecq}{\cosecEL{2}} \newcommand{\cotghq}{\cotghEL{2}} \newcommand{\cosechq}{\cosechEL{2}} \newcommand{\sechq}{\sechEL{2}} \newcommand{\shq}{\shEL{2}} \newcommand{\chq}{\chEL{2}} \newcommand{\arctg}{\mathop{\rm arctg}} \newcommand{\arcsen}{\mathop{\rm arcsen}} \newcommand{\argsh}{\mathop{\rm argsh}} \newcommand{\argch}{\mathop{\rm argch}} \newcommand{\argth}{\mathop{\rm argth}} \newcommand{\Var}{\mathop{\rm Var}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\tr}[1]{ \textnormal{Tr}\left({#1}\right)} \newcommand{\C}{\mathbb{C}} \newcommand{\E}{\mathbb{E}} \newcommand{\H}{\mathbb{H}} \newcommand{\I}{\mathbb{I}} \newcommand{\K}{\mathbb{K}} \newcommand{\N}{\mathbb{N}} \newcommand{\P}{\mathbb{P}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\til}{\sim} \newcommand{\mdc}{\mathop{\rm m.d.c.}} \newcommand{\mmc}{\mathop{\rm m.m.c.}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\dfrc}{\displaystyle\frac} \newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)} \)

terça-feira, 3 de setembro de 2024

Fórmulas de Viéte

Ontem, vi umas fórmulas no facebook. 
Olhando para elas, achei que sabia deduzi-las, e deduzi.

A dedução está feita no meu blog Zona Exacta . 
Depois, notei que a minha cópia (gratuita) do Mathematica, que está incluida no meu Raspberry Pi foi actualizada para o Mathematica 14.




Decidi dar-lhe uso, e escrevi lá as fórmulas e mandei gerar os casos particulares de n=2 até n=10.

Exportei para LaTeX, converti em pdf e juntei à secção de material do blog.

Nisto tudo, só tenho orgulho de ter conseguido deduzir, sem esforço...
Posso ter largado as explicações, mas continuo a ser matemático.

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