Answer:
A
Step-by-step explanation:
We have the equation:
[tex]x^2-2x-2=0[/tex]
We can use the quadratic formula. In this case, a = 1, b = -2, and c = -2. Hence:
[tex]\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{2\pm\sqrt{12}}{2}[/tex]
Simplify:
[tex]\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}[/tex]
Hence:
[tex]\displaystyle x=\frac{2\pm2\sqrt{3}}{2}[/tex]
Divide:
[tex]x=1\pm\sqrt3[/tex]
The correct answer is A.
