Answer:
Correct answer: x₁ = - 3/2 + i √7/2 or x₂ = - 3/2 - i √7/2
Step-by-step explanation:
We will first transform the given equation:
x² + 4x = x - 4 ⇒ x² + 4x - x + 4 = 0 ⇒ x² + 3x + 4 = 0
This equation has no solutions in the set of real numbers but it has in the set of complex numbers.
We will solve this equation as follows:
x² + 3x + 4 = x² + 2 · x · 3/2 + (3/2)² - (3/2)² + 4
the first three terms formed the square of the binomial
(x + 3/2)² - 9/4 + 4 = (x + 3/2)² - 9/4 + 16/4 = (x + 3/2)² + 7/4 =
= (x + 3/2)² - ( - 7/4) = (x + 3/2)² - (i √7/2)²
we gradually transformed the given equation and get the square difference
(x + 3/2)² - (i √7/2)² = (x + 3/2 - i √7/2) · (x + 3/2 - i √7/2)
(x + 3/2 - i √7/2) · (x + 3/2 - i √7/2) = 0 ⇒
x + 3/2 - i √7/2 = 0 or x + 3/2 + i √7/2 = 0 ⇒
x₁ = - 3/2 + i √7/2 or x₂ = - 3/2 - i √7/2
God is with you!!!
