Matematika

Pertanyaan

Tentukan HP :
1/x + 1/y + 1/z = 1/4
1/x + 1/z = 1/6
1/y + 1/z = 1/8

1 Jawaban

  • misalkan 
    m = 1/x
    n = 1/y
    p = 1/z

    maka sistem dapat ditulis
    m + n + p = 1/4 ..............(1)
    m       + p = 1/6 ..............(2)
           n + p = 1/8 ..............(3)

    dari (1) dan (2)
    m + n + p = 1/4
    m       + p = 1/6   - 
    ------------------------
               n = 1/4 - 1/6
               n = 6/24 - 4/24
               n = 2/24
    subtitusikan nilai n = 2/24 ke pers. (3)
    n + p = 1/8
    2/24 + p = 1/8
    p = 3/24 - 2/24
    p = 1/24

    subtitusikan nilai p = 1/24 ke pers. (2)
    m + p = 1/6
    m + 1/24 = 4/24
    m = 3/24

    Jadi
    m = 3/24
    1/x = 3/24
    x = 24/3
    x = 8

    n = 2/24
    1/y = 2/24
    y = 24/2
    y = 12

    p = 1/24
    1/z = 1/24
    z = 24

    Jadi HP : {(8, 12, 24)}

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