Matematika

Pertanyaan

fungsi T:R ----> R ditentukan oleh t(x)=px+q.jika t(5)=25 dan t(-1)=7. tentukan. a.p²+q² b.(p+q)² c.p³+q³ d.(p+q)³-3(pq)

1 Jawaban

  • t(x) = px + q

    t(5) = 5p + q = 25
    t(-1) = - p + q = 7
    --------------------------(-)
    6p = 18
    p = 3
    - p + q = 7
    - 3 + q = 7
    q = 7 + 3
    q = 10

    a) p² + q² = 3² + 10² = 9 + 100 = 109

    b) (p + q)² = (3 + 10)³ = 13² = 169

    c) p³ + q³ = 3³ + 10³ = 27 + 1000 = 1027

    d) (p + q)³ - 3(pq)
    = (3 + 10)³ - 3(3 × 10)
    = 13³ - 3(30)
    = 2197 - 90
    = 2107

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