Question

Calcule as raízes da equação biquadrada x4 + 15x² - 16 = 0​

Answer 1

Resposta:

$S=\{-4i,4i,-1,1\}$

Explicação passo-a-passo:

$x^4+15x^2-16=0\\\\x^2=\frac{-b\pm\sqrt{\Delta} }{2a} \\\\\Delta=15^2-4.1(-16)\\\\\Delta=225+64\\\\\Delta=289\\\\x^2=\frac{-15\pm\sqrt{289} }{2.1}\\\\x^2=\frac{-15\pm17}{2} \\\\x^2=\frac{-32}{2}\\\\x^2=-16\implies x=4i~ou~x=-4i \\\\ou\\\\x^2=\frac{2}{2}\\\\x^2=1\implies~x=1 ~ou~x=-1$