Matematika

Pertanyaan

salah satu akar persamaan( a-1)xkuadrat -18x+6+10a=0 adalah dua kali akar yg alin adalah

1 Jawaban

  • (a-1)x²-18x+6+10a = 0
    a = (a-1)
    b = -18
    c = 6+10a

    x1 = 2x2

    x1+x2 = -b/a
    = 18/a-1
    3x2 = 18/ a-1
    x2 = 6/ a-1

    x1.x2 = c/a
    = 6+10a/ a-1
    2x2² = 6+10a/ a-1
    x2² = 3+5a/ a-1
    6²/(a-1)² =3+5a/ a-1
    36/a-1 = 3+5a
    36 = (a-1)(5a+3)
    = 5a²-2a-3

    5a²-2a-39 = 0
    (5a + 13 )(a - 3) = 0
    a = -13/5 atau a = 3

    a = 3
    2x²-18x+36 = 0
    x²- 9x + 18 = 0

    x2 = 6/ 3-1
    = 3

    x1 = 3.2
    = 6

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