Answer:
[tex]x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}[/tex]
Step-by-step explanation:
Given;
x² - 2x - 1 = 0
Solve by completing the square method;
⇒ take the constant to the right hand side of the equation.
x² - 2x = 1
⇒ take half of coefficient of x = ¹/₂ x -2 = -1
⇒ square half of coefficient of x and add it to the both sides of the equation
[tex]x^2 + (-1)^2 = 1 + (-1)^2[/tex]
[tex](x-1)^2 = 1 + 1\\\\(x-1)^2 = 2\\\\[/tex]
⇒ take the square root of both sides;
[tex]x-1 = +/- \ \ \sqrt{2} \\\\x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}[/tex]
Therefore, option B is the right solution.
