Question

determine quais são as raízes da equação

3 x² - 3√2 x - 9=0
2
 

Answer 1

$\frac{3}{2} \frac{x}{y} x^{2} -X} *x - 9 = 0 \\ \\ \frac{3x^{2} - 3 \sqrt{2} *x - 9}{2}=0 \\ \\ \frac{3x^2 - 6 \sqrt{2}x - 18}{2}=0 \\ \\ 3x^2 - 6 \sqrt{2}x - 18=0$

Para facilitar vamos dividir a equação por 3

$\frac{ 3x^2 - 6 \sqrt{2}x - 18x}{3} = 0 \\ \\ x^{2} -2 \sqrt{2} x - 6 = 0$

$\triangle = {b^2 -4ac}$

$\triangle = (-2 \sqrt{2})^2 - 4 * 1 * -6 \\ \\ \triangle = 4* 2 + 24 \\ \\ \triangle = 8 + 24 \\ \\ \triangle = 32$

$\frac{-b \pm \sqrt{\triangle}}{2*a} \\ \\ \frac{-(-2 \sqrt{2}) \pm \sqrt{32}}{2*1} \\ \\ \frac{2 \sqrt{2} \pm \sqrt{32}}{2} \\ \\ x' = \frac{2 \sqrt{2} + 4\sqrt{2}}{2} \\ \\x' = \frac{6 \sqrt{2}}{2} \\ \\ x' = 3 \sqrt{2} \\ \ \\ \\ \ x'' = \frac{2 \sqrt{2} - 4\sqrt{2}}{2} \\ \\x'' = \frac{-2 \sqrt{2}}{2} \\ \\ x'' = - \sqrt{2}$


S= {$3 \sqrt{2}, - \sqrt{2}$}