Question

РЕШИТЕ УРАВНЕНИЕ:

(x-2)/(x+2) + (x+2)/(x-2) = 3 целых 1/3

Answer 1

ОДЗ
x ≠ - 2; x ≠ 2

3(x - 2)(x - 2) + 3(x + 2)(x + 2) - 10(x - 2)(x + 2) = 0
3(x - 2)^2 + 3(x + 2)^2 - 10(x^2 - 4) = 0
3(x^2 - 4x + 4) + 3(x^2 + 4x + 4) - 10x^2 + 40 = 0
3x^2 - 12x + 12 + 3x^2 + 12x + 12 - 10x^2 + 40 = 0
6x^2 + 24 - 10x^2 + 40 = 0 
- 4x^2 + 64 = 0   /:(-4)
x^2 - 16 = 0
x^2  = 16
x1 = 4
x2 = - 4

ОТВЕТ
- 4; 4