Question

Решите уравнение: 9x2-7x-2=0 7x2-9x+2=0 5x2=12x 7x2-28=0 4x2-x=0 5x2=45 Плиз!помогите пожалуйста очень срочно завтра контрольная у нас!!!

Answer 1

1)X1=1,X2=-2/9
2)X1=1,X2=2/7
3)X=0,X=12/5
4)X=2
5)X=0,X=1/4
6)X=3

Answer 2

Solving the Equations

Let's solve the given equations one by one:

1. Equation 1: 9x^2 - 7x - 2 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, the coefficients are: a = 9, b = -7, c = -2

Substituting these values into the quadratic formula, we get:

x = (-(-7) ± √((-7)^2 - 4 * 9 * (-2))) / (2 * 9)

Simplifying further:

x = (7 ± √(49 + 72)) / 18

x = (7 ± √121) / 18

x = (7 ± 11) / 18

So, the solutions for Equation 1 are: x = (7 + 11) / 18 = 18 / 18 = 1 x = (7 - 11) / 18 = -4 / 18 = -2/9

2. Equation 2: 7x^2 - 9x + 2 = 0

Using the same quadratic formula, we can solve this equation as well:

For the given equation, the coefficients are: a = 7, b = -9, c = 2

Substituting these values into the quadratic formula, we get:

x = (-(-9) ± √((-9)^2 - 4 * 7 * 2)) / (2 * 7)

Simplifying further:

x = (9 ± √(81 - 56)) / 14

x = (9 ± √25) / 14

x = (9 ± 5) / 14

So, the solutions for Equation 2 are: x = (9 + 5) / 14 = 14 / 14 = 1 x = (9 - 5) / 14 = 4 / 14 = 2/7

3. Equation 3: 5x^2 = 12x + 7x^2 - 28 = 0

To solve this equation, we need to combine like terms:

12x + 7x^2 - 28 = 0

Rearranging the equation:

7x^2 + 12x - 28 = 0

We can solve this quadratic equation using the quadratic formula:

For the given equation, the coefficients are: a = 7, b = 12, c = -28

Substituting these values into the quadratic formula, we get:

x = (-12 ± √(12^2 - 4 * 7 * (-28))) / (2 * 7)

Simplifying further:

x = (-12 ± √(144 + 784)) / 14

x = (-12 ± √928) / 14

So, the solutions for Equation 3 are: x = (-12 + √928) / 14 x = (-12 - √928) / 14

4. Equation 4: 4x^2 - x = 0

To solve this equation, we can factor out x:

x(4x - 1) = 0

This equation will be true if either x = 0 or 4x - 1 = 0.

For x = 0, we have one solution.

For 4x - 1 = 0, we can solve for x:

4x = 1 x = 1/4

So, the solutions for Equation 4 are: x = 0 x = 1/4

5. Equation 5: 5x^2 = 45

To solve this equation, we can divide both sides by 5:

x^2 = 9

Taking the square root of both sides, we get:

x = ±√9

So, the solutions for Equation 5 are: x = 3 x = -3

I hope this helps! Let me know if you have any further questions.