Question

Escreva o conjunto solução da equação 9x^4 - 13x^1 + 4 = 0

Answer 1

Olá Thallys.


Se trata de uma equação bi-quadrada. Parece se resolver esse tipo de questão, fazemos uma substituição de variável.

$\mathsf{9x^4-13x^2+4=0}\\\\\mathsf{y=x^2}\\\\\\\mathsf{9y^2-13y+4=0}\\\\\\\mathsf{\Delta=(-13)^2-4\cdot9\cdot4}\\\mathsf{\Delta=169-144}\\\mathsf{\Delta=25}$

$\mathsf{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\\mathsf{y^+=\dfrac{-(-13)+\sqrt{25}}{2\cdot9}\qquad\qquad\qquad\qquad y^-=\dfrac{-(-13)-\sqrt{25}}{2\cdot9}}\\\\\\\mathsf{y^+=\dfrac{13+5}{18}\qquad\qquad\qquad\qquad\qquad\quad~~ y^-=\dfrac{13-5}{18}}\\\\\\\mathsf{y^+=\dfrac{18}{18}\qquad\qquad\qquad\qquad\qquad\qquad\quad~ y^-=\dfrac{8}{18}}\\\\\\\boxed{\mathsf{y^+=1}}\qquad\qquad\qquad\qquad\qquad\qquad\quad\boxed{\mathsf{y^-=\dfrac{4}{9}}}$

$\mathsf{x^2=y}\\\\\\\mathsf{x^2=1}\\\\\mathsf{x=\pm\sqrt{1}}\\\\\mathsf{x=\pm1}\\\\\\\mathsf{x^2=\dfrac{9}{4}}\\\\\mathsf{x=\pm\sqrt{\dfrac{9}{4}}}\\\\\mathsf{x=\pm\dfrac{3}{2}}\\\\\\\boxed{\mathsf{S=\Big\{1,-1,\dfrac{3}{2},-\dfrac{3}{2}\Big\}}}$


Dúvidas? comente.