1. а){2 x-y+3 z = 8
2 x+2 y+z = 1
x+y+z = 4
{2 x-y+3 z = 8
0 x+3 y-2 z = -7
x+y+z = 4
{2 x-y+3 z = 8
0 x+3 y-2 z = -7
0 x+(3 y)/2-z/2 = 0
{2 x-y+3 z = 8
0 x+3 y-2 z = -7
0 x+3 y-z = 0
{2 x-y+3 z = 8
0 x+3 y-2 z = -7
0 x+0 y+z = 7
{2 x-y+3 z = 8
0 x+3 y+0 z = 7
0 x+0 y+z = 7
{2 x-y+3 z = 8
0 x+y+0 z = 7/3
0 x+0 y+z = 7
{2 x+0 y+3 z = 31/3
0 x+y+0 z = 7/3
0 x+0 y+z = 7
{2 x+0 y+0 z = -32/3
0 x+y+0 z = 7/3
0 x+0 y+z = 7
{x+0 y+0 z = -16/3
0 x+y+0 z = 7/3
0 x+0 y+z = 7
Ответ:
| {x = -16/3
y = 7/3
z = 7
б) {2 x+5 y = 3
x-4 y = -5
Отнимем 1/2
{2 x+5 y = 3
0 x-(13 y)/2 = (-13)/2
умножим второе уравнение на -2/13:
{2 x+5 y = 3
0 x+y = 1
Отнимем 5 из 1 уравнения
{2 x+0 y = -2
0 x+y = 1
Поделим 1 уравнение на 2:
{x+0 y = -1
0 x+y = 1
Ответ:
x = -1
y = 1
2. а) 5^(4-8 x) = 1/5Принять взаимные обеих сторон:
5^(8 x-4) = 5
Прологарифмировать основание 5 обеих сторон:
8 x-4 = 1
Добавим 4 к обеим сторонам
8 x = 5
Поделим обе стороны на 8:
Ответ
x = 5/82. б)
(log(x^2-x))/(log(8)) = (log(x+8))/(log(8))
(log(x^2-x))/(log(8))-(log(x+8))/(log(8)) = 0
-(log(x+8)-log(x^2-x))/(log(8)) = 0
log(x+8)-log(x^2-x) = 0
log(x+8)-log(x^2-x) = log(x+8)+log(1/(x^2-x)) = log((x+8)/(x^2-x)):
log((x+8)/(x^2-x)) = 0
(x+8)/(x^2-x) = 1
x+8 = x^2-x
-x^2+2 x+8 = 0
-((x-4) (x+2)) = 0
(x-4) (x+2) = 0
x-4 = 0 or x+2 = 0
x = 4 or x+2 = 0
:
Ответ:
| x = 4 or x = -2
2. в) x^2-6 = 6-x
x^2+x-12 = 0
(x-3) (x+4) = 0
x-3 = 0 or x+4 = 0
x = 3 or x+4 = 0
Ответ:
x = 3 или x = -4