Question

equação bioquadrada:
exercicio

x4 + 3x2- 4

Answer 1

$x^4 + 3x^2-4=0\\\\ \ vamos \ fazer \ x^2 \ = \ g\\\\ x^4 + 3x^2-4=0\\\\ g^2 +3g - 4 = 0$

$\Delta = b^2 - 4ac\\\\ \Delta = 3^2 -4.1.(-4)\\\\ \Delta = 9+16\\\\ \Delta = 25$

$g = \frac{-b+-\sqrt{\Delta}}{2a}\\\\ g = \frac{-3+-\sqrt{25}}{2}\\\\ g= \frac{-3+5}{2}\\\\ g= \frac{2}{2} = 1\\\\ g' = \frac{-3-5}{2}\\\\ g' = \frac{-8}{2} = -4$

Como g = x^2, então:
 
$x^2=1\\\\ x = +-\sqrt{1}\\\\ x=1 \ e \ x=-1$

$x^2=-4\\\\x=+-\sqrt{-4}\\\\x=2i \ e \ x=-2i$

x={1, -1, 2i, -2i}