Question

Pls help i am on a timer

Answer 1

`x = 1 + √(2) \ \ or \ 1- √(2)`

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

`x^2 + (-1)^2 = 1 + (-1)^2`

`(x-1)^2 = 1 + 1\\\\(x-1)^2 = 2\\\\`

⇒ take the square root of both sides;

`x-1 = +/- \ \ √(2) \\\\x = 1 + √(2) \ \ or \ 1- √(2)`

Therefore, option B is the right solution.