Matematika

Pertanyaan

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tolong di banto yaaaaa flisss

1 Jawaban

  • 1) √(x^2 - 3x) ≥ 3√2 ===========> syarat : x^2 - 3x ≥ 0
    (√(x^2 - 3x))^2 ≥ (3√2)^2 ................................ x(x - 3) ≥ 0
    x^2 - 3x ≥ 18 ...................................................... x = 0 atau x = 3
    x^2 - 3x - 18 ≥ 0
    (x - 6)(x + 3) ≥ 0
    x = 6 atau x = -3
    Garis bilangan
    ++++ (-3) ------------------- (6) +++++ => arsir daerah yg positif
    +++++++++ (0) ---- (3) ++++++++++ => arsir daerah yg positif
    Irisan HP = x ≤ -3 atau x ≥ 6

    2) √(x^2 - 3x + 2) ≤ √(x + 7) =====> syarat : 1) x + 7 ≥ 0 => x ≥ -7
    (√(x^2 - 3x + 2))^2 ≤ (√(x + 7))^2 .................... 2) x^2 - 3x + 2 ≥ 0
    x^2 - 3x + 2 ≤ x + 7 ................................................. (x - 2)(x - 1) ≥ 0
    x^2 - 4x - 5 ≤ 0 ........................................................ x = 2 atau x = 1
    (x - 5)(x + 1) ≤ 0
    x = 5 atau x = -1
    Garis bilangan
    +++++++++++++ (-1) ---------------------- (5) +++++ => arsir daerah yg negatif
    ------ (-7) +++++++++++++++++++++++++++++++=> arsir daerah yg positif
    ++++++++++++++++++ (1) --- (2) ++++++++++++ => arsir daerah yg positif
    Irisan HP = -1 ≤ x ≤ 1 atau 2 ≤ x ≤ 5