решите уравнения 1) ||x|-2|=10 2) ||x|-9|=7. Created by znatok1413. algebra-ru

решите уравнения 1) ||x|-2|=10 2) ||x|-9|=7...

znatok1413 @znatok1413

July 2022 1 20 Report

решите уравнения
1) ||x|-2|=10
2) ||x|-9|=7

Answers & Comments

Dимасuk

Verified answer

1. Раскроем сначала внешние модули
1) |x| - 2 = 10
|x| = 10 + 2
|x| = 12
x = -12 или x = 12
2) |x| -2 = -10
|x| = -10 + 2
|x| = -8 - модуль всегда принимает неотрицательные значения.
Ответ: x = -12; 12.

2. Аналогично решим:
1) |x| - 9 = 7
|x| = 16
x = -16 или x = 16
2) |x| - 9 = -7
|x| = 2
x = -2 или x = 2
Ответ: x = -16; -2; 2; 16.

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