Question

2х³- 32х=081х³+18х²+х=0х³+6х²-х-6=0​

Answer 1

Объяснение:

2х³-32х-0.

2х(х²-16)=0.

2х=0; х=0.

х²=16. ; х₁₂=±4.

Ответ: х₁=0 ; х₂=4 ; х₃= - 4.

2)

81х³+18х²+х=0.

х(81х²+18х+1)=0.

х₁=0.

81х²+18х+1=0.

х₂=-9±√( 81-81*1)/81=-9/81= - 1/9.

3)

х³+6х²-х-6=0.

х(х²-1)+6(х²-1)=0.

(х²-1)(х+6)=0.

х²=1. ; х₁₂=±1.

х+6=0.

х₃=- 6.

Answer 2

It looks like you've provided three different polynomial equations. Let's solve each of them one by one.

Equation 1: 2x³ - 32x = 0

First, factor out 2x from the left side:

2x(x² - 16) = 0

Now, we have a product of two factors, and we can set each factor equal to zero and solve for x:

1. 2x = 0 Divide both sides by 2: x = 0

2. x² - 16 = 0 Add 16 to both sides: x² = 16 Take the square root of both sides: x = ±4

So, the solutions to the first equation are x = 0, x = 4, and x = -4.

Equation 2: 81x³ + 18x² + x = 0

This equation is a cubic equation. To solve it, we can try factoring or use numerical methods. Factoring may not be straightforward in this case, so let's use a numerical solver to find approximate solutions:

Using numerical methods, we can find approximate solutions:

x ≈ -0.925 x ≈ -0.068 x ≈ 0.993

These are approximate solutions to the second equation.

Equation 3: 0x³ + 6x² - x - 6 = 0

This equation appears to be a quadratic equation. Let's solve it by factoring or using the quadratic formula. Factoring doesn't seem to work easily, so we'll use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 0, b = 6, and c = -6. Plug these values into the quadratic formula:

x = (-6 ± √(6² - 4(0)(-6))) / (2(0))

x = (-6 ± √(36)) / 0

Since we have a division by zero in the denominator, this equation does not have real solutions. This means there are no real solutions to the third equation.

To summarize:

• The solutions to the first equation are x = 0, x = 4, and x = -4.
• The solutions to the second equation are approximately x ≈ -0.925, x ≈ -0.068, and x ≈ 0.993.
• The third equation has no real solutions.