Предмет: Алгебра, автор: NatsuLucy

log3 (x-1)^2 = 6 Укажите промежуток, которому принадлежит положительный корень уравнения

Ответы

Автор ответа: binamaksimchuk

1

Ответ:

x є [-26;28]

Объяснение:

log₃ (x-1)² = 6

(x-1)² = 3⁶

х²-2х+1=729

х²-2х+1-729=0

х²-2х-728=0

D=(-2)² - 4·1·(-728) = 4 + 2912 = 2916

$x_{1} =\frac{2-54}{2} = -26\\\\\\x_{2} =\frac{2+54}{2} =28$

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