Expressão Algébrica.

por Floral Fury Sex 27 maio 2022, 21:52

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Resp.: Sem gabarito.

Boa noite pessoal!
Como posso fazer essa?
Primeira coisa q fiz, foi fazer as condições de existência para x e tal... só q não consigo ter ideias para fatorar...

Obrigado! cheers

por **Elcioschin** Sex 27 maio 2022, 22:26

x = 1 atende ---> Teste

por Floral Fury Sáb 28 maio 2022, 22:11

Olá Elcio!
Testei e deu certo...

Apenas fico na dúvida se existe outras raízes...
O senhor tem alguma ideia pra calcular elas?
Tentei novamente fatorar, mas sem sucesso

por **Elcioschin** Sáb 28 maio 2022, 22:26

Restrição ---> x é radicando ---> x ≥ 0

Outra restrição ---> Para x = 0 ---> obtém-se 0/0 no 2º membro ---> impossível

Logo ---> x > 0

Ainda não consegui provar a existência ou não de outras raízes.

por Floral Fury Dom 29 maio 2022, 15:05

Entendi, continuarei a tentar fatorar aqui.
Caso consiga, mando aqui no fórum

Obrigado Elcio! cheers

por **petras** Dom 29 maio 2022, 15:10

Floral Fury escreveu:Olá Elcio!
Testei e deu certo...

Apenas fico na dúvida se existe outras raízes...
O senhor tem alguma ideia pra calcular elas?
Tentei novamente fatorar, mas sem sucesso

Usando o artificio no lado esquerdo teremos

[latex] multiplicando~o~lado~esquerdo~por~\dfrac{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}}{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}}\\ (\sqrt{x+\sqrt{x}} - \sqrt{x-\sqrt{x}}) \cdot \dfrac{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}}{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}} = \dfrac{2\cdot \sqrt{x}}{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}}\\ \dfrac{2\cdot \sqrt{x}}{\sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}}} = 2 \cdot \sqrt{\dfrac{x}{x+\sqrt{x}}}\\ igualando~ denominadores : \sqrt{x+\sqrt{x}} + \sqrt{x-\sqrt{x}} = \sqrt{x+ \sqrt{x}}\\ \therefore x - \sqrt{x} = 0~mas x \geq 1 \implies x = 1[/latex]

por Floral Fury Seg 30 maio 2022, 20:03

Olá amigos! Consegui resolver, graças a ajuda de um professor meu.
Irei postar a resolução dele:
---------------------------------------
Jogando o (x + √x) pro outro lado da equação multiplicando:
(x + √x) - √[x(x - 1)] = 2√x
√[x(x - 1)] = x - √x

Elevando ao quadrado e desenvolvendo:
2x(1 - √x) = 0 ---------> x = 0 (não pode) ou x = 1 (aceitável)

Postei para poder contribuir mais ao fórum, com mais essa resolução.

Obrigado! cheers