Matematika

Pertanyaan

Jika x₁ dan x₂ adalah akar-akar persamaan log^2 (x + 2) + log (x + 2)^3 = log 0,01 dengan x₁ > x₂, maka nilai dari x₁ - x₂ = ….

1 Jawaban

  • log² (x + 2) + log (x + 2)³ = log 10^-2
    log² (x + 2) + 3 log (x + 2) + 2 = 0
    (log (x + 2) + 1) (log (x + 2) + 2) = 0

    log (x + 2) + 1 = 0
    log (x + 2) = -1
    x + 2 = 10^-1 = 1/10
    x = 1/10 - 2
    x = -19/10

    log (x + 2) + 2 = 0
    log (x + 2) = -2
    x + 2 = 10^-2
    x = 1/100 - 2
    x = -199/100

    x1 > x2
    x1 = -19/10 = -1,9
    x2 = -199/100 = -1,99

    x1 - x2 = -1,9 - (-1,99) = 0,09

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