Question

Akar - akar persamaan x² - 4x + 6 = 0 adalah x1 dan x2. Tentukan nilai x1³ + x2³

Answer 1

X1 + x2 = -b/a = -(-4) / 1 = 4
x1 x2 = c/a = 6
(x1 + x2)³ = x1³ + 3x1²x2 + 3x1x2² + x2³
(x1 + x2)³ = x1³ + x2³ + 3x1x2(x1+x2)
x1³ + x2³ = (x1 + x2)³ - 3 x1x2 (x1 +x2)
               = (4)³ - 3(6) (4)
               = 64 - 72
               = -8

Answer 2

Dg cara = melengkapi kuadrat sempurna
x² - 4x + 6 = 0
     x² - 4x  = -6
x² - 4x + 4 = -6 + 4
   (x + 2)²   = ± 2
             x = -2 ± 2
x1 = -2 + 2 = 0
x2 = -2 - 2 = -4

nilai
x1³ + x2³ = 0³ + -4³ = -64

(maaf kalau salah)