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Álvaro Antônio de Lacerda Rosário 2025-01-06 19:27:20 -03:00
parent e0361a800a
commit 5fc462265f
2 changed files with 13 additions and 4 deletions
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2
.obsidian/workspace.json vendored
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@ -176,8 +176,8 @@
},
"active": "626a90464762aa2c",
"lastOpenFiles": [
"Matemática/1. Tópicos Fundamentais/Palavras chave.md",
"Matemática/Plano de estudo.md",
"Matemática/1. Tópicos Fundamentais/Palavras chave.md",
"Matemática/1. Tópicos Fundamentais/Exercícios/Aritmética e Álgebra.md",
"Matemática/1. Tópicos Fundamentais/Exercícios",
"Química/Plano de estudo.md",

15
Matemática/1. Tópicos Fundamentais/Exercícios/Aritmética e Álgebra.md
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@ -19,14 +19,23 @@ $$
2a_n = a_{n-1} + a_{n+1}
$$
$$
2a_2 = \dfrac{2}{\sqrt{c} + \sqrt{a}}
$$
$$
\begin{align*}
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
a_1 + a_2 &= \dfrac{1}{\sqrt{b}+\sqrt{c}} + \dfrac{1}{\sqrt{a}+\sqrt{b}} \\
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
&= \dfrac{(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} +
\dfrac{(\sqrt{b}+\sqrt{c})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} \\
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
&= \dfrac{(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} + \dfrac{(\sqrt{b}+\sqrt{c})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} \\
&= \dfrac{\sqrt{a}+ 2\sqrt{b}+\sqrt{c}}{(\sqrt{a}\cdot+\sqrt{b})(\sqrt{b}+\sqrt{c})}
\end{align*}
$$
$$
= \dfrac{\sqrt{a}+ 2\sqrt{b}+\sqrt{c}}{(\sqrt{a}\cdot+\sqrt{b})(\sqrt{b}+\sqrt{c})}
$$