Jumlah kuadrat akar akar persamaan x^2 - x - c = 0 sama dengan jumlah pangkat tiga akar akar persamaan x^2 + 3x + c = 0 nilai c yang memenuhi adalah..

x² - x - c = 0 sama dengan jumlah pangkat tiga akar akar persamaan x² + 3x + c = 0

x1 + x2 = (x'1)³ + (x'2)³
(x'1)³ + (x'2)³
= ((x'1) + (x'2)) * ((x'1)²-x'1x'2 + (x'2)²)
= ((x'1) + (x'2)) * (((x'1)+(x'2))²-2x'1x'2)

x² - x - c = 0
x1 + x2 = -b/a = -(-1)/1 = 1
x1 * x2 = c/a = -c/1 = -c

x² + 3x + c = 0
x'1 + x'2 = -b/a = -3
x'1 * x'2 = c

x1 + x2 = (x'1)³ + (x'2)³
x1 + x2 = ((x'1) + (x'2)) * (((x'1)+(x'2))²-2x'1x'2)

1 = (-3) * ((-3)²-2c)
1 = (-3) *( 9 - 2c)
1 = -27 + 6c
28 = 6c
c = 28/6 = 4(4/6) = 4(⅔)