Question

Помогите пожалуйста

Answer 1

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