Question

Решите уравнения:
1) |x-3|=|x-2|
2)|x-6|=|x-3|

Answer 1

Ответ:

1) x=5/2

2) x=9/2......

Answer 2

|x| = |y| ⇔ x² = y²

(x - y)(x + y) = x² - y²

1

|x - 3| = |x - 2|

(x - 3)² = (x - 2)²

(x - 3)² - (x - 2)² = 0

(x - 3 - x + 2)(x - 3 + x - 2) = 0

-1(2x - 5) = 0

2x - 5 = 0

x = 5/2

2

|x - 6| = |x - 3|

(x - 6)² = (x - 3)²

(x - 6)² - (x - 3)² = 0

(x - 6 - x + 3)(x - 6 + x - 3) = 0

-3(2x - 9) = 0

2x - 9 = 0

x = 9/2