X^2-4x+6 = 21/x^2-4x+10

X² - 4x + 6 = 21 / (x² - 4x + 10)

замена: х² - 4 х = n

n + 6 = 21 / (n + 10)

(n + 6) (n + 10) = 21

n² + 10n + 6n + 60 = 21

n² + 16n + 60 - 21 = 0

n² + 16n + 39 = 0

D = 16² - 4*1*39 = 256 - 156 = 100 = 10²

D> 0

n₁ = (- 16 - 10) / (2 * 1) = - 26/2 = - 13

n₂ = (- 16 + 10) / (2 * 1) = - 6/2 = - 3

x² - 4x = - 13

x² - 4x + 13 = 0

D = (-4) ² - 4*1*13 = 16 - 52 = - 36

D<0 нет решений

х² - 4 х = - 3

х² - 4 х + 3 = 0

D = (-4) ² - 4*1*3 = 16 - 12 = 4 = 2²

D>0

x₁ = (- (-4) - 2) / (2*1) = (4-2) / 2 = 2/2 = 1

x₂ = (- (-4) + 2) / (2*1) = (4 + 2) / 2 = 6/2 = 3

Ответ: х₁ = 1; х₂ = 3.