Question

Resolva as equações biquadradas abaixo em R(numeros reais):

$( x^{2} +2 )^{2} = 2( x^{2} +6)$

Answer 1

E aí mano,

$( x^{2} +2)^2=2( x^{2} +6)\\ (x^2)^2+2\cdot x^2\cdot2+2^2=2x^2+12\\ (x^2)^2+4x^2+4=2x^2+12\\ (x^2)^2+2x^2-8=0\\\\ x^2=k\\\\ k^2+2k-8=0\\\\ k'=2~~e~~k''=-4~~\notin\mathbb{R}\\\\ x^2=k\\ x^2=2\\ x=\pm \sqrt{2}\\\\\\ \large\boxed{\boxed{S=\left\{ \sqrt{2},- \sqrt{2}\right\}}}\\.$

Tenha ótimos estudos =))