Question

4) Resolva em R as equações biquadradas abaixo:​

Answer 1

$\displaystyle \sf 9x^4-13x^2+4 = 0 \\\\ Fa\c camos : \\\\ x^2 = y \\\\ Da{\'i}} : \\\\ 9y^2-13y+4=0 \\\\ y = \frac{-(-13)\pm\sqrt{(-13)^2-4.9.4}}{2.9} \\\\\\ y =\frac{13\pm\sqrt{169-144}}{18}\to y=\frac{13\pm\sqrt{25}}{18} \\\\\\ y = \frac{13\pm5}{18} \to \left\{ \begin{array}{I} \displaystyle \sf y=\frac{13+5}{18} \to y= \frac{18}{18}\to y = 1 \\\\ \displaystyle \sf y=\frac{13-5}{18} \to y= \frac{8}{18}\to y = \frac{4}{9} \end{array} \right$

Desfazendo a troca de variável :  

$\displaystyle \sf x^2 = y \\\\ \left\{ \begin{array}{I} \displaystyle \sf x^2 = 1 \to x= \pm 1 \\\\ \displaystyle \sf x^2=\frac{4}{9} \to x=\pm \frac{2}{3} \end{array} \right$

Portanto as soluções são :

$\boxed{\sf \displaystyle \sf x = \left\{-1,+1, \pm \frac{2}{3} \ \right\} }\checkmark$

letra A