Question

Resolva a Equação Biquadrada:

x^4-17x^2+16=0

^= elevado .

Grato, se alguem souber responder. (:

Answer 1

Dada a equação biquadrada,

$x^4-17x^2+16=0$

faça x²=m:

$(x^2)^2-17x^2+16=0\\ m^2-17m+16=0\\ \Delta=b^2-4ac\\ \Delta=(-17)^2-4\cdot1\cdot16\\ \Delta=289-64\\ \Delta=225\\\\ m= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-(-17)\pm \sqrt{225} }{2\cdot1}= \dfrac{17\pm15}{2}\\\\\\ \begin{cases}m'= \dfrac{17-15}{2}= \dfrac{2}{2}=1\\\\ m''= \dfrac{17+15}{2}= \dfrac{32}{2}=16 \end{cases}$

Voltando à variável original, x²=m:

$x^2=1~~~~~~~~~~~~~~~~~x^2=16\\ x=\pm \sqrt{1}~~~~~~~~~~~~~x=\pm \sqrt{16} \\ x=\pm1~~~~~~~~~~~~~~~~x=\pm4\\\\\\ \Large\boxed{\boxed{\boxed{S=\{1,-1,~4,-4\}}}}.\\.$

Tenha ótimos estudos ;D