Question

(2x-5)²-x≥(2x-1)*(2x+1) Реши Неравенство

Answer 1

Объяснение:

Решение неравенства на фотографии

Answer 2

To solve the inequality, follow these steps:

Step 1: Expand and simplify both sides of the inequality. Step 2: Move all terms to one side to set the inequality to zero. Step 3: Factorize the quadratic equation. Step 4: Find the critical points and intervals where the inequality holds true.

Let's solve it step by step:

Step 1: Expand and simplify both sides of the inequality.

(2x - 5)² - x ≥ (2x - 1) * (2x + 1)

Expanding the left side: (2x - 5) * (2x - 5) - x ≥ (2x - 1) * (2x + 1)

Simplifying: 4x² - 20x + 25 - x ≥ 4x² - 1

Step 2: Move all terms to one side to set the inequality to zero.

4x² - 20x + 25 - x - 4x² + 1 ≥ 0

Step 3: Combine like terms.

-21x + 26 ≥ 0

Step 4: Find the critical points and intervals where the inequality holds true.

To find the critical point, set the left side of the inequality equal to zero:

-21x + 26 = 0

Now, solve for x:

-21x = -26 x = -26 / -21 x ≈ 1.2381

Now, we need to check the intervals determined by the critical point to find where the inequality holds true:

1. x < 1.2381: Pick x = 0 (a value less than 1.2381) -21(0) + 26 = 26 ≥ 0 (True)

2. x > 1.2381: Pick x = 2 (a value greater than 1.2381) -21(2) + 26 = -16 < 0 (False)

So, the solution to the inequality is: x < 1.2381 or x is any real number less than approximately 1.2381.