jika alpha dan beta adalah akar akar persamaan kuadrat x²-6x+3=0 maka 1/alpha+1/beta adalah....

Misal :
Alpha = a
Beta = b

1/a + 1/b
= b/ab + a/ab
= (b + a) / ab

x^2 - 6x + 3
Mengikuti :
ax^2 + bx + c = 0 (ab ini bkn akarnya)
a = 1
b = -6
c = 3

Jmlh kdua akar
= -b/a
= -(-6) / 1
= 6

Hasil kali
= c/a
= 3/1
= 3

Maka :
1/a + 1/b
(b + a) / (ab)
= 6/3
= 2

x^2 - 6x + 3 = 0 => a = 1, b = -6, c = 3
1/Alpha + 1/Beta = -b/c = -(-6)/3 = 2

Kenapa bisa -b/c karena
1/x1 + 1/x2 = (x2 + x1)/(x1.x2) = (-b/a)/(c/a) = -b/c