Question

(x-6)^2=(x-3)^2 и (x-9)^2=(x+4)^2

Answer 1

1)

x²-12x+36=x²-6x+9

-12x+6x=9-36

-6x=-27

x=9/2 (или 4,5)

2)

x²-18x+81=x²+8x+16

-18x-8x=16-81

-26x=-65

x= 5/2 (или 2,5)

Answer 2

(x - 6)² = (x - 3)²

x² - 12x + 36 = x² - 6x + 9

- 12x + 36 = - 6x + 9

- 12x + 6x = 9 - 36

- 6x = - 27

x = 9/2 = 4,5

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(x - 9)² = (x + 4)²

x² - 18x + 81 = x² + 8x + 16

- 18x + 81 = 8x + 16

- 18x - 8x = 16 - 81

- 26x = - 65

x = 5/2 = 2,5

Answer 3

To solve the equations:

1. (x-6)^2 = (x-3)^2

Expanding both sides of the equation:

x^2 - 12x + 36 = x^2 - 6x + 9

Subtracting x^2 from both sides:

-12x + 36 = -6x + 9

Subtracting 9 from both sides:

-12x + 27 = -6x

Adding 6x to both sides:

-12x + 6x + 27 = 0

Combining like terms:

-6x + 27 = 0

Subtracting 27 from both sides:

-6x = -27

Dividing by -6:

x = 4.5

2. (x-9)^2 = (x+4)^2

Expanding both sides of the equation:

x^2 - 18x + 81 = x^2 + 8x + 16

Subtracting x^2 from both sides:

-18x + 81 = 8x + 16

Subtracting 16 from both sides:

-18x + 65 = 8x

Adding 18x to both sides:

-18x + 18x + 65 = 0

Combining like terms:

65 = 18x

Dividing by 18:

x = 65/18

So the solutions to the equations are x = 4.5 and x = 65/18.