jika x1 dan x2 adalah akar dari persamaan 2x^2 - 5x + 6 =0 maka x1/x2 + x2/x1

Mapel : Matematika
Kelas : X SMA
Bab : Persamaan Kuadrat

Pembahasan :
2x² - 5x + 6 = 0

Teorema Vietta
X1 + X2 = -b/a
X1 + X2 = -(-5)/2
X1 + X2 = 5/2

X1 . X2 = c/a
X1 . X2 = 6/2
X1 . X2 = 3

Maka :
X1/X2 + X2/X1
= (X1² + X2²)/(X1 . X2)
= [(X1 + X2)² - 2(X1 . X2)]/(X1 . X2)
= [(5/2)² - 2(3)]/3
= [(25/4) - 6]/3
= [(25 - 24)/4]/3
= (1/4)/3
= 1/12

2x² - 5x + 6 = 0
a = 2
b = -5
c = 6

x1 + x2 = -b/a = -(-5)/2 = 5/2
x1 . x2 = c/a = 6/2 = 3



x1/x2 + x2/x1
= (x1² + x2²)/(x1 . x2)
= ((x1 + x2)² - 2 x1 . x2)/3
= ((5/2)² - 2 . 3)/3
= (25/4 - 6)/3
= (25/4 - 24/4)/3
= (1/4)/3
= 1/4 . 1/3
= 1/12