diketahui akar akar persamaan kuadrat 3x^2 - 18x + 9 = 0 adalah x1 dan x2. nilai dari x1^3 + x2^3 =

Bab Persamaan Kuadrat
Matematika SMP Kelas VIII

3x² - 18x + 9 = 0
a = 3; b = -18; c = 9

x1³ + x2³ = (x1 + x2)³ (x1² - x1 . x2 . + x2²)
x1³ + x2³ = (-b/a)³ . ((x1² + x2²) - c/a))
x1³ + x2³ = (-(-18)/3) . (((x1 + x2)² - 2 . x1 . x2) - 9/3)
x1³ + x2³ = 6 . ((6² - 2 . 3) - 3)
x1³ + x2³ = 6 . (36 - 6 - 3)
x1³ + x2³ = 6 . 27
x1³ + x2³ = 162

# terima kasih #

Matematika VIII SMP
→→ Persamaan Kuadrat ←←

Pembahasan :
3x² - 18x + 9 = 0
3(x² - 6x + 3) = 0
x² - 6x + 3 = 0

Berdasarkan Teorema Vietta
X1 + X2 = -b/a
X1 + X2 = -(-6)/1
X1 + X2 = 6

X1 . X2 = c/a
X1 . X2 = 3/1
X1 . X2 = 3

Maka...
X1³ + X2³
= (X1 + X2)(X1² - X1.X2 + X2²)
= (X1 + X2)(X1² + X2² - X1.X2)
= (X1 + X2)[{(X1 + X2)² - 2X1.X2} - X1.X2]
= (6)[{(6)² - 2(3)} - 3]
= 6[{36 - 6} - 3]
= 6[30 - 3]
= 6(27)
= 162