Matematika

Pertanyaan

apabila x,y,z membentuk barisan arimatika dgn x+y+zadlh 15 dan xy=15 tentukan nilai 2x-y+z=...........

1 Jawaban

  • misal, x = a
    y = a + b
    z = a + 2b

    x + y + z = a + a + b + a + 2b = 3a + 3b = 15
    3a + 3b = 15
    3(a + b) = 15
    a + b = 5

    xy = a(a + b) = a(5) = 5a = 15
    5a = 15
    a = 3

    a + b = 5
    3 + b = 5
    b = 2

    2x - y + z = 2a - (a + b) + (a + 2b)
    = 2(3) - (3 + 2) + (3 + 2(2))
    = 6 - 5 + 7
    = 8

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