Question

26. 1) x²-3x = 0; 3) 0,7x-1,4x² = 0; 2) 5x + 2x² = 0; 4) 1/7x2-3 1/7x2 = 0​

Answer 1

Ответ:

1) x = 0 або x - 3 = 0, тобто x = 3
2) x = 0 і x = -5/2
3) x = 0 і x = 0.5
4) x = 0

Объяснение:

1) x² - 3x = 0

x - спільний член

x(x - 3) = 0

x = 0 або x - 3 = 0, тобто x = 3

2) 5x + 2x² = 0

x(5 + 2x) = 0

a) x = 0

b) 5 + 2x = 0

2x = -5

x = -5/2

знову два розв'язки: x = 0 і x = -5/2

3) 0.7x - 1.4x² = 0

x(0.7 - 1.4x) = 0

a) x = 0

b) 0.7 - 1.4x = 0

-1.4x = -0.7

x = -0.7 / (-1.4)

x = 0.5

x = 0 і x = 0.5

4) (1/7)x^2 - 3(1/7)x^2 = 0

(1/7 - 3/7)x^2 = 0 - спростили вираз, спiльний множник 1/7

a) (1/7 - 3/7)x^2 = 0

-2/7x^2 = 0

x^2 = 0

x = 0

b) (1/7 - 3/7)x^2 = 0

-2/7x^2 = 0

x = 0

Answer 2

It looks like you've provided four different quadratic equations. Let's solve each of them:

1. x² - 3x = 0

To solve this equation, you can factor out an x: x(x - 3) = 0

Now, set each factor equal to zero:

1. x = 0
2. x - 3 = 0

For the second equation: x = 3

So, the solutions are x = 0 and x = 3.

2. 5x + 2x² = 0

This equation can be factored as follows: x(5 + 2x) = 0

Now, set each factor equal to zero:

1. x = 0
2. 5 + 2x = 0

For the second equation: 2x = -5 x = -5/2

So, the solutions are x = 0 and x = -5/2.

3. 0.7x - 1.4x² = 0

First, let's factor out 0.7x: 0.7x(1 - 2x) = 0

Now, set each factor equal to zero:

1. 0.7x = 0
2. 1 - 2x = 0

For the first equation: 0.7x = 0 x = 0

For the second equation: 1 - 2x = 0 -2x = -1 x = 1/2

So, the solutions are x = 0 and x = 1/2.

4. (1/7)x² - (31/7)x² = 0

This equation can be simplified by combining like terms: (1/7 - 31/7)x² = 0 (-30/7)x² = 0

Now, set the equation equal to zero: (-30/7)x² = 0

To solve for x, divide both sides by (-30/7): x² = 0 / (-30/7) x² = 0

To solve for x, take the square root of both sides: x = ±√0 x = 0

So, the only solution is x = 0.

In summary, the solutions for each equation are:

1. x = 0 and x = 3
2. x = 0 and x = -5/2
3. x = 0 and x = 1/2
4. x = 0