Question

Найдите решения системы

Answer 1

Объяснение:

{1/х + 1/у = 5/6

{х+у=5 Х=5-у

1/(5-у) + 1/у - 5/6=0

(6у+6(5-у) - 5у(5-у))/(6y(5-y))=0

(6у+30-6у-25у+5у²)/(6y(5-y))=0

(5у²-25у+30)/(6y(5-y))=0

5y²-25y+30=0

y²-5y+6=0

D=(-5)²-4•1•6=25-24=1

y1=(5-1)/2=2

y2=(5+1)/2=3

x1=5-2=3

x2=5-3=2

(3;2) ; (2;3)

проверка:

(3;2)

{1/3+1/2=5/6

{3+2=5

{5/6=5/6

{5=5

(2;3)

{1/2+1/3=5/6

{2+3=5

{5/6=5/6

{5=5

ответ: (3;2) ; (2;3)