X² + X + 1 = 0

 How to solve x²+x+1=0 ?

➡️ The equation x² + x + 1 = 0 is a quadratic equation. To solve it, you can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In the given equation, a = 1, b = 1, and c = 1. Plugging these values into the quadratic formula, we get:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying further:

x = (-1 ± √(1 - 4)) / 2

x = (-1 ± √(-3)) / 2

Since the term inside the square root is negative, we can conclude that the given equation has no real solutions. The solutions are complex numbers.

Hence, the solutions to the equation x² + x + 1 = 0 are:

x = (-1 + i√3) / 2

x = (-1 - i√3) / 2

where i represents the imaginary unit (√-1).