Question

(x²-2x)²-3x²+6x-4=0 ​

Answer 1

Дано уравнение (x²-2x)²-3x²+6x-4=0.

Выделим повторяющийся элемент (x²-2x):

(x²-2x)²-3(x²-2x)-4=0.

Сделаем замену (x²-2x) = а.

а² - 3а - 4 = 0, D = 9 + 16 = 25.  a1 = (3 - 5)/2 = -1.  a2 = (3 + 5)/2 = 4.

Обратная замена:

x² - 2x = -1, x² - 2x + 1 = 0. D = 4 - 4 = 0. x1 = 2/2 = 1.

x² - 2x = 4.  x² - 2x - 4 = 0. D = 4 + 16 = 20. √D = √20 = 2√5.

x2 = (2 - 2√5)/2 = 1 - √5.

x3 =  (2 + 2√5)/2 = 1 + √5.

Ответ: х1 = 1, х2 = 1 - √5, х3 = 1 + √5.

Answer 2

To solve the equation (x² - 2x)² - 3x² + 6x - 4 = 0, you can follow these steps:

1. Expand and simplify the left side of the equation: (x² - 2x)² - 3x² + 6x - 4 = (x⁴ - 4x³ + 4x²) - 3x² + 6x - 4

2. Combine like terms: x⁴ - 4x³ + 4x² - 3x² + 6x - 4 = x⁴ - 4x³ + x² + 6x - 4

3. Set the equation equal to zero: x⁴ - 4x³ + x² + 6x - 4 = 0

Now, you can attempt to factor or solve this equation. Factoring a quartic equation can be complex, and there's no general formula for solving quartic equations, so you may need to use numerical methods or a computer algebra system to find the solutions. You can try factoring or use numerical methods like the Newton-Raphson method to approximate the solutions. If you have specific values or a range for x, you can also use a graphing calculator or software to find the approximate solutions.