Question

(100 Баллов) Решите неравенство методом интервалов:

Answer 1

$x \geqslant 4 {x}^{2} - 2x + 2 \\ 0 \geqslant 4 {x}^{2} - 3x + 2$
нет корней

Answer 2

Solving the Inequality Using Interval Method

To solve the given inequality using the interval method, we need to find the intervals where the inequality is true. Let's solve the inequality step by step:

1. \(x^2 - 5x + 6 > 0\): - Factorizing the quadratic equation: \(x^2 - 5x + 6 = 0\) gives us \((x - 3)(x - 2) = 0\). - Setting each factor equal to zero, we get \(x - 3 = 0\) and \(x - 2 = 0\). - Solving for \(x\), we find \(x = 3\) and \(x = 2\). - Now, we can create intervals using these values: \((-\infty, 2) \cup (2, 3) \cup (3, +\infty)\).

2. \(-3 < x < -2\): - This is a simple inequality with a range of values between -3 and -2, excluding both endpoints. - The solution can be written as \(-3 < x < -2\).

3. \(-\infty < x < 7\) or \(x > 7\): - This inequality has two parts: \(x < 7\) and \(x > 7\). - The solution can be written as \((-\infty, 7) \cup (7, +\infty)\).

Therefore, the solution to the given inequality using the interval method is:

\((-\infty, 2) \cup (2, 3) \cup (3, +\infty)\) or \(-3 < x < -2\) or \((-\infty, 7) \cup (7, +\infty)\)