Question

Rozwiąż równanie.
a) (x - 2)(x + 2) + 4 = (x - 2)²
c) (x - 1)² – (-1)² = (x - 2)(2 + x)
b) (x + 1)² = 7 + (x − 3)(x + 3)
d) x - (x – 3)(3 + x) = 10 - (x - 2)²​

Answer 1

a)

(x - 2)(x + 2) + 4 = (x - 2)²

x² - 4 + 4 = x² - 4x + 4

x² - x² + 4x = 4

4x = 4   |:4

x = 1

c)

(x - 1)² - (- 1)² = (x - 2)(2 + x)

x² - 2x + 1 - 1 = x² - 4

x² - 2x - x² = - 4

- 2x = - 4   |:(-2)

x = 2

b)

(x + 1)² = 7 + (x - 3)(x + 3)

x² + 2x + 1 = 7 + x² - 9

x² + 2x - x² = - 2 - 1

2x = - 3   |:2

x = - ³/₂

x = - 1 ¹/₂

d)

x - (x - 3)(3 + x) = 10 - (x - 2)²​

x - (x² - 9) = 10 - (x² - 4x + 4)

x - x² + 9 = 10 - x² + 4x - 4

x - x² + x² - 4x = 6 - 9

- 3x = - 3   |:(-3)

x = 1