Question

log x+2 (x2-1) = log x+2 (x+5)

Answer 1

Răspuns:

x₂ = 3

Explicație pas cu pas:

logₓ₊₂(x²-1) = logₓ₊₂(x+5)

Conditii:

x²-1 > 0   x² > 1  => x ∈ (-∞ ; -1) ∪ (1 ; +∞)

x+5 > 0 => x > -5

x+2 > 0 => x > -2

x+2 ≠ 1 => x ≠ -1 =>

x ∈ (1 ; +∞) =>

x²-1 = x+5 => x²-x-6 = 0 => x₁,₂ = [1±√(1+24)]/2 =>

x₁,₂ = (1±5)/2 => x₁ = -2 nu convine; x₂ = 3