Question

розв'язати рівняння (x²-3x)²-14(x²-3x)+40=0​

Answer 1

(x² - 3x)² - 14(x² - 3x) + 40 = 0

Замена переменной: x² - 3x = t

t² - 14t + 40 = 0

D = (-14)² - 4 * 40 = 196 - 160 = 36

√D = √36 = 6

t₁ = (14 - 6) / 2 = 8 / 2 = 4

t₂ = (14 + 6) / 2 = 20 / 2 = 10

Обратная замена:

1) x² - 3x = 4

x² - 3x - 4 = 0

D = (-3)² + 4 * 4 = 9 + 16 = 25

√D = √25 = 5

x₁ = (3 - 5) / 2 = - 2 / 2 = - 1

x₂ = (3 + 5) / 2 = 8 / 2 = 4

2) x² - 3x = 10

x² - 3x - 10 = 0

D = (-3)² + 4 * 10 = 9 + 40 = 49

√D = √49 = 7

x₁ = (3 - 7) / 2 = - 4 / 2 = - 2

x₂ = (3 + 7) / 2 = 10 / 2 = 5

Ответ: x₁ = - 2; x₂ = - 1; x₃ = 4; x₄ = 5.