1)
х² - 4х + 3 = 0
х² - 4х + 3 = ( х² - 4х + 4) - 4+ 3 = (х-2)² - 1
(х-2)² - 1 = 0
√(х-2)² = √1
х-2 = 1 => x₁ = 3
х-2 = - 1 => x₂ = 1
2)
х² - 6х + 5 = 0
х² - 6х + 5 = ( х² - 6х + 9) - 9 + 5 = (х-3)² - 4
(х-3)² - 4 = 0
√(х-3)² = √4
х-3 = 2 => x₁ = 5
х-3 = - 2 => x₂ = 1
3)
x² + 8x -20 = 0
х² + 8х - 20 = ( х² + 8х + 16) - 16 - 20 = (х+4)² - 36
(х-4)² - 36 = 0
√(х-4)² = √36
х-4 = 6 => x₁ = 10
х-4 = - 6 => x₂ = - 2
4)
х² + 12х + 32 = 0
х² + 12х + 32 = ( х² + 12х + 36) - 36 + 32 = (х+6)² - 4
(х+6)² - 4 = 0
√(х+6)² = √4
х+6 = 2 => x₁ = - 4
х+6 = - 2 => x₂ = - 8
5)
x² - 2x - 15 = 0
х² - 2х - 15 = ( х² - 2х + 1) - 1 - 15 = (х-1)² - 16
(х-1)² - 16 = 0
√(х-1)² = √16
х-1 = 4 => x₁ = 5
х-1 = - 4 => x₂ = - 3
6)
х² - 4х - 45 = 0
х² - 4х - 45 = ( х² - 4х + 4) - 4 - 45 = (х-2)² - 49
(х-2)² - 49 = 0
√(х-2)² = √49
х-2 = 7 => x₁ = 9
х-2 = - 7 => x₂ = - 5