Question

2. Confirm that 1+V5 and 1 - V5 are the correct roots for x2 – 2x – 4 = 0.

Answer 1

see explanation

Explanation:

Given

x² - 2x - 4 = 0 ( add 4 to both sides )

x² - 2x = 4

To solve use the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = 4 + 1

(x - 1)² = 5 ( take the square root of both sides )

x - 1 = ±
`√(5)` ( add 1 to both sides )

x = 1 ±
`√(5)`, thus

x = 1 +
`√(5)` or x = 1 -
`√(5)`