Решите систему уравнений

log4 (x+y) = 2

log3 x + log3 y = 2 + log3 7

X + y = 4²

x + y = 16

log3 x + log3 y = 2 + log3 7

2 = log3 9

log3 x + log3 y = log3 9 + log3 7

log3 (x*y) = log3 (9*7)

x*y = 63

x=63/y

x + y = 16 63/y + y - 16 = 0

(63/y + y - 16 = 0) * y

63 + y² - 16y = 0

D = (b) ²-4*a*c = (-16) ² - 4*1*63 = 256 - 252 = 4

y1,2 = (-b + & - √D) / 2a

y1 = (16 - 2) / 2*1 = 14/2 = 7

y2 = (16 + 2) / 2 = 18/2 = 9

x1 + y1 = 16

x1 = 16 - y1 = 16 - 7 = 9

x1 = 9,

x2 + y2 = 16

x2 = 16 - y2 = 16 - 9 = 7

x2 = 7.

Ответ (7; 9), (9; 7)