Matematika

Pertanyaan

soal no 8 gimana caranya?
soal no 8 gimana caranya?

1 Jawaban

  • misal alfa = a dan beta = b
    a) I) a² - ab + b² = a² + b² - ab
    = (a + b)² - 2ab - ab
    = (a + b)² - 3ab
    II)
    dari persamaan kuadrat pertama
    a + b = -2/1 = -2
    a.b = m/1 = m
    dari persamaan kuadrat kedua
    a³.b³ = 512/1 = 512
    (a.b)³ = 512
    a.b = ³√512
    a.b = 8
    m = 8
    a³ + b³ = -n/1 = -n
    (a + b)³ - 3ab(a + b) = -n
    (-2)³ - 3(8)(-2) = -n
    -8 + 48 = -n
    40 = -n
    n = -40

    b) persamaan kuadrat x² - (x1+x2)x + x1.x2 = 0
    x1 + x2 = a / (a+b) + b/(a+b)
    = (a+b) / (a+b)
    = 1
    x1.x2 = a / (a+b) × b(a+b)
    = a.b / (a+b)²
    = (-2/4) / (-1/4)²
    = (-1/2) / (1/16)
    = (-1/2) × (16/1)
    = -8
    x² - 1x + (-8) = 0
    x² - x - 8 = 0