Решите неравенство x^2> - 4x-1

Question

Решите неравенство x^2> - 4x-1

Answer 1

X² + 4x + 1 > 0
D = 16 - 4 = 12

x₁ = (-4 - 2√3)/2 = -2 - √3

x₂ = -2 + √3

Ответ: x ∈ (-∞; - 2 - √3) U (-2 + √3; +∞)

Answer 2

Х^2+4х+1>0
(x-x1)(x-x2)>0
Тогда х€(-inf;x1)U(x2;+inf).
Найдём х1 и х2.
D=16-4=12 => x1=-4-2sqrt(3)/2=-2-sqrt(3), x2=-2+sqrt(3), т.е.,
х€(-inf;-2-sqrt(3))U(-2+sqrt(3);+inf).