Question

1)(5x+3)^2=5x+3; 2)(3x-8)^2=3x^2-8x; 3)(3x+10)^2=3x+10; 4)(4x+5)^2=5x^2+4x; помагите пожалуйста

Answer 1

1))
25х^2+30х+9=5х+3
25х^2+25х+6=0
Найдем дискриминант квадратного уравнения:

D = b^2 - 4ac = 25^2-4·25·6 = 625 - 600 = 25
Так как дискриминант больше нуля то, квадратное уравнение имеет два действительных корня:

x1 = (-25 - √25)/2×25= (-25 - 5) /50=-30 /50= -0.6

x2 =(-25 + √25)/50 =(-25 + 5)/50=-20 /50=
-0.4

2))9х^2-48х+64=3х^2-8х
6х^2-40х+64=0
Найдем дискриминант квадратного уравнения:

D=b^2- 4ac=(-40)^2- 4·6·64=1600-1536 = 64
Так как дискриминант больше нуля то, квадратное уравнение имеет два действительных корня:

x1=(40 - √64)/6×2 =(40 - 8)/12=32/12=8/3

x2=(40 + √64)/12 =(40 + 8)/12 = 48/12= 4

Answer 2

Solution to the Equations

Let's solve the given equations one by one:

1) (5x+3)^2 = 5x+3

To solve this equation, we can expand the left side and simplify:

(5x+3)^2 = (5x+3)(5x+3) = 25x^2 + 30x + 9

Now, we have the equation: 25x^2 + 30x + 9 = 5x + 3

Simplifying further, we get: 25x^2 + 25x + 6 = 0

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 25, b = 25, and c = 6. Substituting these values into the formula, we get:

x = (-25 ± √(25^2 - 4 * 25 * 6)) / (2 * 25)

Simplifying further, we get:

x = (-25 ± √(625 - 600)) / 50

x = (-25 ± √25) / 50

x = (-25 ± 5) / 50

This gives us two solutions:

x = (-25 + 5) / 50 = -20 / 50 = -0.4

x = (-25 - 5) / 50 = -30 / 50 = -0.6

Therefore, the solutions to the equation (5x+3)^2 = 5x+3 are x = -0.4 and x = -0.6.

2) (3x-8)^2 = 3x^2 - 8x

To solve this equation, we can expand the left side and simplify:

(3x-8)^2 = (3x-8)(3x-8) = 9x^2 - 24x + 64

Now, we have the equation: 9x^2 - 24x + 64 = 3x^2 - 8x

Simplifying further, we get: 6x^2 - 16x + 64 = 0

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 6, b = -16, and c = 64. Substituting these values into the formula, we get:

x = (-(-16) ± √((-16)^2 - 4 * 6 * 64)) / (2 * 6)

Simplifying further, we get:

x = (16 ± √(256 - 1536)) / 12

x = (16 ± √(-1280)) / 12

Since the discriminant is negative, the equation has no real solutions.

Therefore, the equation (3x-8)^2 = 3x^2 - 8x has no real solutions.

3) (3x+10)^2 = 3x + 10

To solve this equation, we can expand the left side and simplify:

(3x+10)^2 = (3x+10)(3x+10) = 9x^2 + 60x + 100

Now, we have the equation: 9x^2 + 60x + 100 = 3x + 10

Simplifying further, we get: 9x^2 + 57x + 90 = 0

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 9, b = 57, and c = 90. Substituting these values into the formula, we get:

x = (-57 ± √(57^2 - 4 * 9 * 90)) / (2 * 9)

Simplifying further, we get:

x = (-57 ± √(3249 - 3240)) / 18

x = (-57 ± √9) / 18

x = (-57 ± 3) / 18

This gives us two solutions:

x = (-57 + 3) / 18 = -54 / 18 = -3

x = (-57 - 3) / 18 = -60 / 18 = -3.33

Therefore, the solutions to the equation (3x+10)^2 = 3x + 10 are x = -3 and x = -3.33.

4) (4x+5)^2 = 5x^2 + 4x

To solve this equation, we can expand the left side and simplify:

(4x+5)^2 = (4x+5)(4x+5) = 16x^2 + 40x + 25

Now, we have the equation: 16x^2 + 40x + 25 = 5x^2 + 4x

Simplifying further, we get: 11x^2 + 36x + 25 = 0

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 11, b = 36, and c = 25. Substituting these values into the formula, we get:

x = (-36 ± √(36^2 - 4 * 11 * 25)) / (2 * 11)

Simplifying further, we get:

x = (-36 ± √(1296 - 1100)) / 22

x = (-36 ± √196) / 22

x = (-36 ± 14) / 22

This gives us two solutions:

x = (-36 + 14) / 22 = -22 / 22 = -1

x = (-36 - 14) / 22 = -50 / 22 = -2.27

Therefore, the solutions to the equation (4x+5)^2 = 5x^2 + 4x are x = -1 and x = -2.27.

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