Question

9b² + 4c² + 2 > или = 6b - 4c Помогите пожалуйста!!!)))

Answer 1

9b+4c+2=18b-8c+2=12bc

Answer 2

Problem Statement

You are looking for a detailed explanation of the inequality 9b² + 4c² + 2 > or = 6b - 4c.

Solution

To solve this inequality, we can follow these steps:

1. Move all the terms to one side of the inequality to set it equal to zero. - Subtract 6b and add 4c to both sides of the inequality: 9b² + 4c² + 2 - 6b + 4c > or = 0

2. Simplify the equation by combining like terms: 9b² - 6b + 4c² + 4c + 2 > or = 0

3. Factor out common terms, if possible. However, in this case, the equation cannot be factored further.

4. Determine the discriminant to analyze the quadratic equation. The discriminant is calculated using the formula: b² - 4ac. In this case, a = 9, b = -6, and c = 4c² + 4c + 2. - Calculate the discriminant: (-6)² - 4 * 9 * (4c² + 4c + 2)

5. Analyze the discriminant to determine the nature of the solutions: - If the discriminant is greater than zero, the quadratic equation has two real solutions. - If the discriminant is equal to zero, the quadratic equation has one real solution. - If the discriminant is less than zero, the quadratic equation has no real solutions.

6. Solve the inequality using the discriminant: - If the discriminant is greater than or equal to zero, the inequality is satisfied. - If the discriminant is less than zero, the inequality is not satisfied.

Let's calculate the discriminant and analyze the inequality further.

Calculating the Discriminant

The discriminant is calculated as follows: (-6)² - 4 * 9 * (4c² + 4c + 2)

Simplifying the expression: 36 - 144(4c² + 4c + 2)

Expanding the expression: 36 - 576c² - 576c - 288

Combining like terms: -576c² - 576c - 252

Analyzing the Discriminant

The discriminant is -576c² - 576c - 252. Since this is a quadratic equation, we can analyze the discriminant to determine the nature of the solutions.

Unfortunately, we cannot determine the exact nature of the solutions without knowing the value of c. However, we can make some general observations:

- If the discriminant is greater than or equal to zero (-576c² - 576c - 252 >= 0), the inequality is satisfied. - If the discriminant is less than zero (-576c² - 576c - 252 < 0), the inequality is not satisfied.

To determine the exact nature of the solutions, we need to know the value of c. Without that information, we cannot provide a definitive answer.

Please provide the value of c so that we can further analyze the inequality and provide a more accurate solution.