Ответ:
x=15; y=12
Пошаговое объяснение:
x+y>0; x-y>0
log₆(x+y)=3log₆(x-y)
log₆(x+y)=4log₆3-log₆(x-y)
_____________________
log₆(x+y)=log₆(x-y)³
log₆(x+y)+log₆(x-y)=log₆3⁴
_____________________
x+y=(x-y)³
log₆(x+y)(x-y)=log₆81
_____________________
x+y=(x-y)³
(x+y)(x-y)=81⇒x+y=81/(x-y)
_____________________
81/(x-y)=(x-y)³
(x-y)⁴=81, x-y>0⇒x-y=3
x+y=3³=27
__________________
x-y=3
x+y=27
_________
(x+y)+(x-y)=3+27
(x+y)-(x-y)=27-3
____________
2x=30
2y=24
________
x=15
y=12