Question

solve for x the quadratic equation x^2-4x-8=0​

Answer 1

Answer:

x = 2 ± 2√3

Step-by-step explanation:

Method I :-

x² - 4x - 8 = 0

x = (-b ± √(b²- 4ac)) ÷ 2a --------> Formula for finding roots of a quadratic

a = 1, b = -4, c = -8

x = (4 ± √(16 + 32)) ÷ 2

  = (4 ± √48) ÷ 2

  = (4 ± 4√3) ÷ 2

∴ x = 2 ± 2√3

Method II :-

x² - 4x - 8 = 0

x² - 4x + 4 - 4 - 8 = 0

Using the identity a² - 2ab + b² = (a - b)²

(x - 2)² - 12 = 0

(x - 2)² - (√12)² = 0

(x - 2)² - (2√3)² = 0

Using identity a² - b² = (a + b)(a - b)

(x - 2 - 2√3)(a - 2 + 2√3) = 0

∴ x = 2 ± 2√3

Hope this helps! :)