Question

(2x-1)²-10(2x-1)+21=0

Answer 1

(2x-1)²-10(2x-1)+21=0

4x²-4x+1-20x+10+21=0

4x² - 24x + 32 = 0

x² - 6x + 8 = 0

D = 36 - 32 = 4

x₁₂ = (6 +- 2)/2 = 4   2

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или

2х - 1 = t

t² - 10t + 21 = 0

D = 100 - 84 = 16

t₁₂ = (10 +- 4)/2 = 3   7

2x₁ - 1 = 7   2x₁ = 8   x₁ = 4

2x₂ - 1 = 3   2x₂ = 4  x₂ = 2

ответ x = {2, 4}

Answer 2

Ответ:

(2х-1)*(2х-1-10)+21=0

(2х-1)*(2х-11)+21=0

4х²-22х-2х+11+21=0

4х²-24х+32=0

х²-6х+8=0

х1 = 2

х2 = 4

Answer 3

To solve the quadratic equation (2x - 1)² - 10(2x - 1) + 21 = 0, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = -10, and c = 21. Now, plug these values into the quadratic formula:

x = (-(-10) ± √((-10)² - 4(1)(21))) / (2(1))

x = (10 ± √(100 - 84)) / 2

x = (10 ± √16) / 2

x = (10 ± 4) / 2

Now, you have two possible solutions for x:

1. x = (10 + 4) / 2 = 14 / 2 = 7
2. x = (10 - 4) / 2 = 6 / 2 = 3

So, the solutions to the equation (2x - 1)² - 10(2x - 1) + 21 = 0 are x = 7 and x = 3.