Question

решить систему уравнений

Answer 1

log(2) x + log(2) (y - 1) = 1

log(2) x * log(2) (y - 1) = -2

x > 0  y > 1

log(2) x = u

log(2)(y - 1) = t

u + t = 1

ut = -2

ну Можно виета вспомнить

u = 1 - t

t(1 - t) = -2

t² - t - 2 = 0

D = 1 + 8 = 9

t12 = (1 +- 3)/2 = 2   -1

1. t1 = -1

u1 = 2

log(2) x = -1        x = 1/2

log(2) ( y - 1) = 2    y = 5

2. t2 = 2

u2 = -1

log(2) x = 2         x = 4

log(2)(y - 1) = -1     y = 3/2

ответ (4, 3/2) (1/2, 5)