Question

x²-2x-2=0.........................​

Answer 1

Explicação passo-a-passo:

$\sf x^2-2x-2=0$

$\sf \Delta=(-2)^2-4\cdot1\cdot(-2)$

$\sf \Delta=4+8$

$\sf \Delta=12$

$\sf x=\dfrac{-(-2)\pm\sqrt{12}}{2\cdot1}=\dfrac{2\pm2\sqrt{3}}{2}$

$\sf x'=\dfrac{2+2\sqrt{3}}{2}~\rightarrow~\red{x'=1+\sqrt{3}}$

$\sf x"=\dfrac{2-2\sqrt{3}}{2}~\rightarrow~\red{x"=1-\sqrt{3}}$

$\sf S=\{1-\sqrt{3},1+\sqrt{3}\}$

Answer 2

Explicação passo-a-passo:

Equação do segundo grau :

$\sf{ \pink{ x^2 - 2x - 2 = 0 } }$

$\iff \sf{ x^2 - 2x + 1 - 3 = 0 }$

$\iff \sf{ (x - 1)^2~=~ 3 }$

$\iff \sf{ x - 1~=~\pm \sqrt{3} }$

$\iff \sf{ x~-1~=~-\sqrt{3}~\vee~x-1~=~\sqrt{3} }$

$\iff \sf{ x~=~1- \sqrt{3}~\vee~x~=~\sqrt{3}+1 }$

$\green{ \sf{Sol: \left\{ 1-\sqrt{3}~;~\sqrt{3}+1 \right\} \longleftarrow Resposta } }$

Espero ter ajudado bastante!)