Question

quais são as raízes de:
$4x {}^{4} - 37x {}^{2} + 9 = 0$

Answer 1

$4 x^{4} -37 x^{2} +9 = 0$

Usando Y = x²

$4 y^{2} - 37y + 9 = 0$

Fazemos delta

$(b)^{2} -4ac \\ (37)^{2}-4.(4).(9) \\ 1.369-144 \\ 1225$

Usaremos na formula de bhaskara

$\frac{(37)+- \sqrt{delta}}{2.4} \\ \\ \frac{37+- \sqrt{1225} }{8} \\ \\ \frac{37+-35}{8} \\ \\ y1= \frac{37+35}{8} = \frac{72}{8} = 9 \\ \\ y2= \frac{37-35}{8} = \frac{2}{8} = \frac{1}{4}$

Agora como x²=y


$x^{2} = y \\ \\ x^{2} =9 \\ x= \sqrt{9} \\ x=3 \\ x= +-3 \\ \\ x^{2} =1/4 \\ x= \sqrt{ \frac{1}{4} } \\ x= \frac{1}{2} \\ x=+- \frac{1}{2}$