Question

Rezolvati inecuatia:

Answer 1

Răspuns:

Explicație pas cu pas:

(4x-1) / (x²+7x+6) < -1 <=>

(4x-1) / (x²+7x+6) + 1 < 0 <=>

(4x-1) / (x²+7x+6) + ˣ²⁺⁷ˣ⁺⁶⁾1  < 0 <=>

(x²+11x+5) / (x²+7x+6) < 0

x²+11x+5 = 0 => x₁,₂ = [(-11±√(121-20)]/2 = (-11±√101)/2

x₁ = (-11-√101)/2 ≈ -10,5

x₂ = (-11 +√101)/2 ≈ - 0,5

x²+7x+6 = x²+6x+x+6 = x(x+6)+(x+6) = (x+6)(x+1)

x²+7x+6 = 0 => x₁ = -6 ; x₂ = -1

                             x I -∞       x₁    -6              -1    x₂              +∞

                 x²+11x+5 I ++++++0-----------------------0+++++++++++

                  x²+7x+6 I+++++++++++0------------0++++++++++++++

(x²+11x+5)/(x²+7x+6) I ++++++0------I++++++++I---0+++++++++++

=> x ∈ ((-11-√101)/2 ; -6) ∪ (-1 ; (-11+√101)/2)