Question

resolva a equação
$x {}^{4} = \frac{7x {}^{2} }{3} - \frac{2}{3}$

Answer 1

$x^4=\frac{7x^2}{3}-\frac{2}{3}\\ \\ 3x^4=7x^2-2\\ \\ 3x^4-7x^2+2=0\\ \\ \boxed{y=x^2}\\ \\ 3x^2-7x+2=0\\ \\ \Delta=(-7)^2-4.3.2=49-24=25\\ \\ y=\frac{7\pm5}{6}\\ \\ y_1=\frac{1}{3}\\ \\ y_2=2\\ \\ x^2=\frac{1}{2}\Rightarrow x=\pm \frac{\sqrt2}{2}\\ \\ x^2=2\Rightarrow x=\pm\sqrt2$