2x - 1 = (x - 2)²
2x - 1 = x² - 4x + 4
x² - 4x + 4 - 2x + 1 = 0
x² - 6x + 5 = 0
(x - 5)(x - 1) = 0
1) x₁ - 5 = 0; x₁ = 5
2) x₂ - 1 = 0; x₂ = 1 - не подходит 1 ∉ [2; +∞)
ответ: х = 5
2x - 1 = (x - 2)²
2x - 1 = x² - 4x + 4
x² - 4x + 4 - 2x + 1 = 0
x² - 6x + 5 = 0
(x - 5)(x - 1) = 0
1) x₁ - 5 = 0; x₁ = 5
2) x₂ - 1 = 0; x₂ = 1 - не подходит 1 ∉ [2; +∞)
ответ: х = 5