Решение
1 - sin(x/2 + π/3) = 0
sin(x/2 + π/3) = 1
x/2 + π/3 = π/2 + 2πk,k ∈Z
x/2 = π/2 - π/3 + 2πk,k ∈Z
x/2 = π/6 + 2πk, k∈Z
x = π/3 + 4πk, k∈Z
lg(x² - 2) = lgx
ОДЗ: x² - 2 > 0, x² > 2, x∈ (- ∞; - √2) (√2; + ∞)
x² - 2 = x
x² - x - 2 = 0
x₁ = - 1 не принадлежит ОДЗ x∈ (- ∞; - √2) (√2; + ∞)
x₂ = 2
Ответ: х = 2