Question

(x⁴-6) (6-x-2 x²) =0​

Answer 1

я не знаю точно но

вроде ответ :2

Answer 2

To solve the equation (x⁴ - 6)(6 - x - 2x²) = 0, you can use the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. So, you can set each factor equal to zero and solve for x:

1. Set the first factor, x⁴ - 6, equal to zero: x⁴ - 6 = 0

2. Add 6 to both sides of the equation: x⁴ = 6

3. Take the fourth root of both sides to isolate x: x = ±∛6

Now, set the second factor, 6 - x - 2x², equal to zero:

6 - x - 2x² = 0

4. Rearrange the terms: 2x² + x - 6 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2, b = 1, and c = -6. Plugging these values into the quadratic formula:

x = (-1 ± √(1² - 4(2)(-6))) / (2(2))

x = (-1 ± √(1 + 48)) / 4

x = (-1 ± √49) / 4

x = (-1 ± 7) / 4

So, you have two solutions:

x₁ = (7 - 1) / 4 = 6/4 = 3/2 x₂ = (-1 - 7) / 4 = -8/4 = -2

Therefore, the solutions to the equation (x⁴ - 6)(6 - x - 2x²) = 0 are:

x = ±∛6, x = 3/2, and x = -2.