Найдите корень уравнения: a) √x² - 297 = 12 б) √x² + 184 = 25 в) √x² + 25 = 13 г) √4x + 20 = 10

Решение:

1. a) √x² - 297 = 12
   \( x^2 - 297 = 12^2 \)
   \( x^2 - 297 = 144 \)
   \( x^2 = 144 + 297 \)
   \( x^2 = 441 \)
   \( x = \pm \sqrt{441} \)
   \( x = \pm 21 \)
2. б) √x² + 184 = 25
   \( x^2 + 184 = 25^2 \)
   \( x^2 + 184 = 625 \)
   \( x^2 = 625 - 184 \)
   \( x^2 = 441 \)
   \( x = \pm \sqrt{441} \)
   \( x = \pm 21 \)
3. в) √x² + 25 = 13
   \( x^2 + 25 = 13^2 \)
   \( x^2 + 25 = 169 \)
   \( x^2 = 169 - 25 \)
   \( x^2 = 144 \)
   \( x = \pm \sqrt{144} \)
   \( x = \pm 12 \)
4. г) √4x + 20 = 10
   \( 4x + 20 = 10^2 \)
   \( 4x + 20 = 100 \)
   \( 4x = 100 - 20 \)
   \( 4x = 80 \)
   \( x = \frac{80}{4} \)
   \( x = 20 \)

Ответ: а) ±21; б) ±21; в) ±12; г) 20.