Question

X² - x + 1 < 0 решить неравенство​

Answer 1

Ответ:

Оскільки старший коефіцієнт а додатний, ліва частина нерівності завжди додатна, отже, твердження хибне для всіх значень х

Answer 2

To solve the inequality x² - x + 1 < 0, we can follow these steps:

1. Factorize the quadratic expression if possible. However, in this case, the expression cannot be easily factorized.

2. Use the quadratic formula to find the roots of the quadratic equation x² - x + 1 = 0. The quadratic formula states that for an equation in the form ax² + bx + c = 0, the roots can be found using the formula:

   x = (-b ± √(b² - 4ac)) / (2a)

   For the equation x² - x + 1 = 0, the values of a, b, and c are: a = 1, b = -1, and c = 1. Plugging these values into the quadratic formula, we get:

   x = (-(-1) ± √((-1)² - 4(1)(1))) / (2(1)) = (1 ± √(1 - 4)) / 2 = (1 ± √(-3)) / 2

   Since the discriminant (b² - 4ac) is negative, the quadratic equation has no real solutions. Therefore, there are no real roots for x² - x + 1 = 0.

3. Determine the behavior of the quadratic expression x² - x + 1 for different values of x. We can observe that the coefficient of x² is positive (a = 1), indicating an upward-opening parabola. Furthermore, the discriminant is negative, indicating that the quadratic expression is always positive. Therefore, x² - x + 1 > 0 for all real values of x.

4. Thus, x² - x + 1 < 0 has no solution in the set of real numbers. The inequality is not satisfied for any real value of x.

In conclusion, the inequality x² - x + 1 < 0 has no solutions in the real number system.