Объяснение:
{ Х + у = 8;
Log12 x = 1 - log12 y;
{ x = 8 - y;
Log12 x = 1 - log12 y;
{ x = 8 - y;
Log12 (8 - y) = 1 - log12 y;
{ x = 8 - y;
Log12 (8 - y) = log12 12 - log12 y;
{ x = 8 - y;
Log12 (8 - y) = log12 (12/y);
1) Log12 (8 - y) = log12 (12/y);
ОДЗ: 8 - y > 0;
12/y > 0;
{ - y > - 8;
y не равен 0;
{ y < 8;
y не равен 0;
Тогда:
8 - y = 12/y;
y * (8 - y) = 12;
- y ^ 2 + 8 * y - 12 = 0;
y1 = 6;
y2 = 2;
Отсюда:
x1 = 8 - y1 = 8 - 6 = 2;
x2 = 8 - y2 = 8 - 2 = 6;
ответ: (2; 6) и (6; 2).
