Matematika

Pertanyaan

nomor 8 pakai caranya...
nomor 8 pakai caranya...

1 Jawaban

  • 6x² + x - 2 = 0
    a = 6
    b = 1
    c = -2

    x1 + x2 = -b/a
    x1 + x2 = -1/6
    x1 = -1/6 - x2

    x1 . x2 = c/a
    (-1/6 - x2) . x2 = -2/6
    -1/6x2 - x2² = -1/3 (kali 6 kedua ruas)
    -x2 - 6x2² = -2
    0 = 6x2² + x2 - 2
    0 = 6x2² - 3x2 + 4x2 - 2
    0 = 3x2(2x2 - 1) + 2(2x2 - 1)
    0 = (2x2 - 1)(3x2 + 2)

    2x2 - 1 = 0
    2x2 = 1
    x2 = 1/2
    atau
    3x2 + 2 = 0
    3x2 = -2
    x2 = -2/3

    Jika x2 = 1/2, maka:
    x1 = -1/6 - x2
    x1 = -1/6 - 1/2
    x1 = -1/6 - 3/6
    x1 = -4/6 = -2/3

    Jika x2 = -2/3, maka:
    x1 = -1/6 - x2
    x1 = -1/6 - (-2/3)
    x1 = -1/6 + 2/3
    x1 = -1/6 + 4/6
    x1 = 3/6 = 1/2

    Karena x1 > x2, maka nilai x1 = 1/2 dan x2 = -2/3
    x1 - x2 = 1/2 - (-2/3)
    x1 - x2 = 1/2 + 2/3
    x1 - x2 = 3/6 + 4/6
    x1 - x2 = 7/6 = 1 1/6

    Jawaban: C