Persamaan kuadrat 3x2-5x+1=0 mempunyai akar x1 dan x2 persamaan kuadrat yang akarnya 1/x1-1 dan 1=x2-1

Bab Persamaan Kuadrat
Matematika SMP Kelas VIII

3x² - 5x + 1 = 0
a = 3; b = -5; c = 1

penjumlahan akar
1/(x1 - 1) + 1/(x2 - 1) = (x2 - 1 + x1 - 1)/(x1 - 1) (x2 - 1) → perkalian akar
1/(x1 - 1) + 1/(x2 - 1) = (-b/a - 2) / (x1 . x2 - (x1 . x2) + 1)
1/(x1 - 1) + 1/(x2 - 1) = (5/3 - 2) / (1/3 - 5/3 + 1)
1/(x1 - 1) + 1/(x2 - 1) = -1/3 / -1/3
1/(x1 - 1) + 1/(x2 - 1) = 1

perkalian akar
1/(x1 - 1) . 1/(x2 - 1) = 1/ (-1/3) = -3

x² - (x1 + x2) x + (x1 . x2) = 0
x² - x - 3 = 0