Question

(х²-2х)²+12(х²-2х)+11=0 2х³-3х²-3х+2=0

Answer 1

Ответ:

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Объяснение:

Answer 2

(x² - 2x)² + 12(x² - 2x) + 11 = 0             |  x² - 2x = y

y² + 12y + 11 = 0                      D = b²-4ac = 144-44 = 100

y₁₂ = (-b±√D)/2a

y₁ = (-12+10):2 = -1

y₂ = (-12-10):2 = -11

x² - 2x = -1                 x² - 2x = -11

х² - 2х + 1 = 0           x² - 2x + 11 = 0

D = 4-4 = 0               D = 4-44 = -40        

x = 1                            ∅          

Ответ: {1}

2х³ - 3х² - 3х + 2 = 0

2(x³ + 1) - 3x(x + 1) = 0

2(х + 1)(x² - x + 1) - 3x(x + 1) = 0

(x + 1)(2x² - 5x + 2) = 0

x₁ = -1

2x² - 5x + 2 = 0             D = b²-4ac = 25-16 = 9

x₂₃ = (-b±√D)/2a

x₂ = (5+3):4 = 2

x₃ = (5-3):4 = 0,5

Ответ: {-1; 0,5; 2}

Answer 3

To solve the given equations:

1. (x² - 2x)² + 12(x² - 2x) + 11 = 0:

Let's simplify the equation step by step:

Let's substitute y = x² - 2x: y² + 12y + 11 = 0

Now, we can solve this quadratic equation for y. We can either factorize it or use the quadratic formula:

Factorizing: (y + 1)(y + 11) = 0

Setting each factor equal to zero: y + 1 = 0 or y + 11 = 0

Solving for y: y = -1 or y = -11

Substituting y back: x² - 2x = -1 or x² - 2x = -11

Now we solve each equation separately:

For x² - 2x = -1:

x² - 2x + 1 = 0 (x - 1)² = 0

Taking the square root of both sides: x - 1 = 0 x = 1

For x² - 2x = -11:

x² - 2x + 11 = 0

Using the quadratic formula: x = (-(-2) ± √((-2)² - 4(1)(11))) / (2(1)) x = (2 ± √(4 - 44)) / 2 x = (2 ± √(-40)) / 2 x = (2 ± 2i√10) / 2 x = 1 ± i√10

Therefore, the solutions to the equation (x² - 2x)² + 12(x² - 2x) + 11 = 0 are: x = 1, 1 + i√10, and 1 - i√10.

2. 2x³ - 3x² - 3x + 2 = 0:

This is a cubic equation, and finding its exact solutions can be more complicated. We can attempt to find rational solutions using the Rational Root Theorem.

The possible rational roots of the equation are given by the factors of the constant term (2) divided by the factors of the leading coefficient (2). So, the possible rational roots are ±1 and ±2.

By testing these values, we find that x = 1 is a root of the equation.

Using synthetic division or long division, we can divide the given equation by (x - 1):

(2x³ - 3x² - 3x + 2) ÷ (x - 1) = 2x² - x - 2

Now we have a quadratic equation 2x² - x - 2 = 0.

We can solve this quadratic equation using factorization, completing the square, or the quadratic formula.

By factoring: (2x + 1)(x - 2) = 0

Setting each factor equal to zero: 2x + 1 = 0 or x - 2 = 0

Solving for x: 2x = -1 or x = 2

For 2x = -1: x = -1/2

For x - 2 = 0: x = 2

Therefore, the solutions to the equation 2x³ - 3x² - 3x + 2 = 0 are: x = -1/2, 1, and 2.