Question

Решите системы уравнений 100б​

Answer 1

ОДЗ: x>0, y>0

Log5(x)+y=7

x^y= 5^12

log5(x) = 7-y

x= 5^(7-y)

(5^(7-y))^y= 5^12

7y-y^2=12

y^2-7y+12=0

D= 49-48=1

y1= (7+1)/2= 4

y2= (7-1)/2= 3

x1= 5^3= 125

x2= 5^4= 625

Ответ; (125;4), (625;3)