Question

X elevado à quarta menos 16 x ao quadrado igual a zero

Answer 1

$x^4-16x^2=0\\Equa\c c\~ao~~~Biquadrada.~~~~Seja~~~x^2=y\\\\ y^2 - 16y=0~~~~~Coloque~~~em~~~Evid\^encia:\\\\ y(y-16)=0\\\\ \underline{y'=0}\\\\y-16 = 0\to~~~\underline{y=16}\\\\\\ Agora, ~~~se ~~~x^2=y,~~~ent\~ao:\\\\\\ x^2=y'\to~~~x^2=0\to~~~x= \pm \sqrt{0} \to~~~x=0\\\\x^2=y''\to~~~x^2=16\to~~~x=\pm \sqrt{16} \to~~~x=\pm 4\to\\\\\\\\ \large\boxed{\boxed{S=\{~ -4~;~0~;~4 ~\}}}$