Question

X elevado a quarta menos 8 x ao quadrado mais 16 igual a zero

Answer 1

$x^4-8x^2+16=0\\\\Chamando\;A=x^2:\\\\A^2-8A+16=0\\\\Bhaskara\\\\\Delta = (-8)^2-4.1.16\\\Delta=64-64\\\Delta=0\\\\A_1=\frac{8+\sqrt{0}}{2.1}=\frac{8}{2}=4\\\\A_2=\frac{8-\sqrt{0}}{2.1}=\frac{8}{2}=4$

Se A1 e A2 valem 4, vamos calcular os valors de x:

$x=\pm\sqrt{A_1}\\\\x=\pm\sqrt{4}\\\\x=\pm2\\\\\\x=\pm\sqrt{A_2}\\\\x=\pm\sqrt{4}\\\\x=\pm2$

Portanto, as 4 raizes da equação são: -2 , -2 , 2 , 2