Решите систему уравнений log4 (x+y)=2 log3 x + log3 - вопрос №4233236795610 от salavat5sal 15.04.2022 11:26

Question

Математика: Решите систему уравнений log4 (x+y)=2 log3 x + log3 y = 2 + log3 7

salavat5sal · Answer

X + y = 4²x + y = 16log3 x + log3 y = 2 + log3 72 = log3 9log3 x + log3 y = log3 9 + log3 7log3 (x*y) = log3 (9*7)x*y = 63x=63/yx + y = 16     63/y + y -16 = 0(63/y + y -16 = 0)*y63 + y² - 16y = 0D = (b)²-4*a*c = (-16)² - 4*1*63 = 256 - 252 = 4y1,2 = (-b + & - √D)/2ay1 = (16 - 2)/2*1 = 14/2 = 7y2= (16 + 2)/2 = 18/2 = 9x1 + y1 = 16x1 = 16 -y1 = 16 - 7 = 9x1 = 9,x2 + y2 = 16x2 = 16 - y2 = 16 - 9 = 7x2 = 7.ответ (7 ; 9),(9 ; 7)...