Question

2. Pemme yparteme: x+6= √8-6x-x¹ A)-2 B) 2 D)3 E) -45​

Answer 1

Ответ:

Пошаговое объяснение:

Правильный ответ: Б) 2. Уравнение является квадратным уравнением и может быть решено с помощью квадратной формулы. Квадратичная формула: x = [-b ± √(b²-4ac)] / 2a. В этом случае a = -1, b = 6 и c = -8. Включение этих чисел в формулу дает [-6 ± √(-36 + 32)] / 2(-1), что упрощается до 2.

Answer 2

To solve the equation x + 6 = √(8 - 6x - x²), we'll follow these steps:

Step 1: Move all terms to one side of the equation to isolate the radical. x + 6 + x² + 6x - √(8 - 6x - x²) = 0

Step 2: Rearrange the terms. x² + 7x + 6 - √(8 - 6x - x²) = 0

Step 3: Square both sides of the equation to eliminate the square root. (x² + 7x + 6 - √(8 - 6x - x²))² = 0

Expanding the squared term: x⁴ + 14x³ + 13x² + (12 - 2√(8 - 6x - x²))x + (36 + 12√(8 - 6x - x²) + (8 - 6x - x²)) = 0

Simplifying further: x⁴ + 14x³ + 13x² + 12x - 2x√(8 - 6x - x²) + 36 + 12√(8 - 6x - x²) + 8 - 6x - x² = 0

Step 4: Combine like terms. x⁴ + 14x³ + 12x² + 5x + 44 + 10√(8 - 6x - x²) - 2x√(8 - 6x - x²) - x² = 0

Step 5: Simplify the square root terms. x⁴ + 14x³ + 12x² + 5x + 44 + (10 - 2)x√(8 - 6x - x²) - x² = 0

x⁴ + 14x³ + 12x² + 5x + 44 + 8x√(8 - 6x - x²) - x² = 0

Step 6: Group like terms together. (x⁴ + 14x³ + 12x² - x²) + (5x + 8x√(8 - 6x - x²)) + 44 = 0

x⁴ + 14x³ + 11x² + (5x + 8x√(8 - 6x - x²)) + 44 = 0

Step 7: Factor out common terms. x²(x² + 14x + 11) + x(5 + 8√(8 - 6x - x²)) + 44 = 0

Step 8: Notice that x = -2 is a root of the equation. Plugging in x = -2 into the original equation: -2 + 6 = √(8 - 6(-2) - (-2)²) 4 = √(8 + 12 - 4) 4 = √16 4 = 4

Since -2 is a valid solution, option A) -2 is correct.

Therefore, the correct answer is A) -2.