Question

√4x-x² + √5+4x-x² + √12+4x-x² = 9​

Answer 1

Ответ:

область визначення: х≥0

Перетин з віссю ординат (0, √5 + 2√3)

Объяснение:

графік

Answer 2

To solve the equation √(4x - x²) + √(5 + 4x - x²) + √(12 + 4x - x²) = 9, we can start by isolating one of the radicals on one side of the equation and then square both sides multiple times to eliminate the radicals.

Here's the step-by-step solution:

1. Subtract √(5 + 4x - x²) and √(12 + 4x - x²) from both sides of the equation to isolate √(4x - x²): √(4x - x²) = 9 - √(5 + 4x - x²) - √(12 + 4x - x²)

2. Square both sides of the equation to eliminate the first radical: (√(4x - x²))^2 = (9 - √(5 + 4x - x²) - √(12 + 4x - x²))^2

Simplifying the right side: 4x - x² = 81 - 18√(5 + 4x - x²) - 18√(12 + 4x - x²) + 5 + 4x - x² - 36√(5 + 4x - x²)(12 + 4x - x²)

3. Combine like terms and isolate the remaining radicals: 0 = 86 - 36√(5 + 4x - x²) - 36√(12 + 4x - x²) - 36√(5 + 4x - x²)(12 + 4x - x²)

4. Square both sides again to eliminate the remaining radicals: 0 = 7396 - 5184√(5 + 4x - x²) - 5184√(12 + 4x - x²) - 20736(5 + 4x - x²)

Simplifying the equation: 20736(5 + 4x - x²) = 7396 - 5184√(5 + 4x - x²) - 5184√(12 + 4x - x²)

5. Move all terms with radicals to one side of the equation: 20736(5 + 4x - x²) + 5184√(5 + 4x - x²) + 5184√(12 + 4x - x²) = 7396

6. Square both sides once more: (20736(5 + 4x - x²) + 5184√(5 + 4x - x²) + 5184√(12 + 4x - x²))^2 = 7396^2

Expanding and simplifying the equation: 428867584(5 + 4x - x²) + 20736(5 + 4x - x²)√(5 + 4x - x²) + 20736(12 + 4x - x²)√(12 + 4x - x²) + 5184^2(5 + 4x - x²) = 54653536

7. Collecting like terms: (449631744 + 20736√(5 + 4x - x²) + 20736√(12 + 4x - x²)) + (428867584 + 20736√(5 + 4x - x²) +