Autor: Larissa | Publicado: 2011-10-14T17:02:00-07:00

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Equações Biquadradas Na Equação Biquadrada para resolvê-la temos que antes transformar o X4 em X2 como no exemplo:
Ex.: x4 – 10x2 + 9 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (x2)2 – 10x2 + 9 = 0 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X2 = y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y2 - 10y + 9 = 0 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y2 = - 10y + 9 = 0 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ∆= (-10)2 – 4.1.9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ∆= 100 – 36 = 64&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y = - (- 10) ± √64&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2.1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Y= 10 ± 8 = x| = 9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x|| = 1
Mas nessa aqui não é o final, pois só descobrimos o valor de Y e o objetivo é descobrir o valor de X. Então voltamos lá atrás no que aprendemos na Equação do 20 Grau incompleta.
X2= y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;X2 = 9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x2 = 1X2 = ± √9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x2 = ± √1X = ± 3 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x = ± 1
S= {-3, -1, 1,3}&nbsp;
Obs.: Na equação do 1 grau temos no máximo uma solução, na equação do 20 grau temos até duas soluções e na equação biquadrada temos até quatro soluções. Como está no exemplo acima.