Відповідь:
x=4.099494563
y=0.8976946457
Покрокове пояснення:
log_8 (x+y)+log_8 (x-y) = 1/3log_2 (x+y)+1/3log_2 (x-y)=4/3
log_2 (x+y)+log_2 (x-y)=4
log(x^2-y^2)=log_2(2^4)
x^2-y^2=16
6^(log_4(x+y)=8
(6^(log_2(x+y))^(1/2)=8
6^(log_2(x+y)=64
log_6(6^(log_2(x+y)) =log_6 (64)
log_2(x+y)=6/log_2(6)=2.3211168434
Подставим в предидущее уравнение
log_2 (x+y)+log_2 (x-y)=4
log_2 (x-y)=4-2.3211168434=1.678883156
x-y=2^1.678883156
x-y=3.201799918
x=y+3.201799918
Подставим x в
x^2-y^2=16
(y+3.201799918)^2-y^2=6.403599836y+10.251522714=16
y=0.8976946457
Подставим y в x=y+3.201799918
x=0.8976946457+3.201799918
x=4.099494563
x=1-2/3
x=3/3-2/3
x=1/3
2) 4/5+x=1/2
x=1/2-4/5
x=5/10-8/10
x= -3/10
3) 7/20+x=1/3
x=1/3-7/20
x=20/60-21/60
x= -1/60
4)-5/16+x=17/18
x= 17/18+5/16
x= 136/144+45/144
x= 181/144
x= 1 37/144
5) x-17/18=-10/9
x= -10/9+17/18
x= -20/18+17/18
x = -3/18
x= -1/6
6) 2/5-x=1/3
-x = 1/3-2/5
-x = 5/15 - 6/15
-x= -1/15
x= 1/15
7) -8/9-x=17/18
-x = 17/18+8/9
-x= 17/18+16/18
-x = 33/18
x= -1 15/18
x = -1 5/6
8) -7/9-x=13/18
-x = 13/18+7/9
-x = 13/18+14/18
-x= 27/18
-x = 1 9/18
-x= 1 1/2
x= -1 1/2