Autor: Larissa | Publicado: 2011-10-14T17:40:00-07:00

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Equações Irracionais
São todas as equações que têm a variável sobre o radical.1 Passo – Temos que tirar o radical para poder resolver. O contrário da radiciação é a potenciação por isso elevamos a raiz de acordo com seu índice. Assim conseguimos tirar o radical. Veja no exemplo abaixo:
Ex.:&nbsp;&nbsp; √x+4&nbsp; -3 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (√x+4)2 = 32&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X+4 = 9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;X = 9-4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X = 5Testando raiz:√5+4&nbsp; -3 = 0√9&nbsp;&nbsp; -3 = 0&nbsp;3 – 3 = 0 0 = 0 (v)S={5}
Obs.: Algumas das equações irracionais a solução que dá não é realmente o resultado. Por isso testamos a raiz. Substituindo o X pelo valor que deu na solução.
Ex.2: (√x+5)2 = (x-1)2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X+5 = x2 – 2x + 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -x2 + x + 2x + 5 – 1 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -x2 + 3x + 4 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ∆= 32 – 4.(-1).4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ∆= 9 + 16 = 25&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X = -3 ± 5 = x| = -1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; x|| = 4Testando as raízes:
X = -1
√-1+5 = -1-1&nbsp; &nbsp; &nbsp; √4 = -2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 = -2 (F)
X = 4
√4+5 = 4-1&nbsp;&nbsp;&nbsp; √9 = 3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3 = 3 (V)S= {4}
Obs.: Só pode ser a solução o valor que corresponder com o outro. Como no exemplo acima.2 não é igual a -2 isso é falso. Já 3 é igual a 3 isso é verdadeiro. Então o número que vai para a solução é o 4. Tem um detalhe você não pode errar na hora da solução tem que prestar atenção porque é o valor que der no X.