Под корнем х+2-под корнем х-6=2

sqrt (х + 2) - sqrt (х - 6) = 2;

(x + 2) - 2 * sqrt (x + 2) * sqrt (x - 6) + (x - 6) = 4;

2x - 4 - 2 * sqrt (x + 2) * sqrt (x - 6) = 4;

2x - 4 - 4 = 2 * sqrt (x + 2) * sqrt (x - 6);

2x - 8 = 2 * sqrt (x + 2) * sqrt (x - 6);

x - 4 = sqrt (x + 2) * sqrt (x - 6);

x^2 - 8x + 16 = (x + 2) * (x - 6);

x^2 - 8x + 16 = x^2 - 6x + 2x - 12;

-8x + 6x - 2x = - 16 - 12;

-4x = - 28;

x = - 28/-4;

x = 7.

Ответ: 7.

Проверка: sqrt (7 + 2) - sqrt (7 - 6) = 2;

sqrt (9) - sqrt (1) = 2;

3 - 1 = 2 - верно.