Question

X elevado a 2 - (3+ raíz quadrada de 2)x +3 raíz quadrada de 2 =0

Answer 1

$x^2-\left(3+\sqrt{2}\right)x+3\sqrt{2}=0\\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\sqrt{\left(-3-\sqrt{2}\right)^2-12\sqrt{2}}=3-\sqrt{2}\\\mathrm{Expandir}\:\left(-3-\sqrt{2}\right)^2-12\sqrt{2}:\quad 11-6\sqrt{2}\\ =\sqrt{11-6\sqrt{2}}\\ \mathrm{Fatorar}\:11-6\sqrt{2}:\quad \left(\sqrt{2}-3\right)^2\\ =\sqrt{\left(\sqrt{2}-3\right)^2}\\ \left(\sqrt{2}-3\right)^2=\left(3-\sqrt{2}\right)^2\\ =\sqrt{\left(3-\sqrt{2}\right)^2}\\ =\frac{-\left(-3-\sqrt{2}\right)-\left(3-\sqrt{2}\right)}{2}\\ \mathrm{Expandir}\:-\left(-3-\sqrt{2}\right)-\left(3-\sqrt{2}\right):\quad 2\sqrt{2}$

$=\frac{2\sqrt{2}}{2}\\ \mathrm{Dividir:}\:\frac{2}{2}=1\\ =\sqrt{2}\\ \mathrm{As\:solucoes\:para\:a\:equacao\:de\:segundo\:grau\:sao:\:}\\ x=3,\:x=\sqrt{2}$

Bons Estudos!