Persamaan kuadratX²+y²=40;xy=12

x^2 + y^2 = 40.. xy = 12==» y = 12/x
x^2 + (12/x)^2 = 40
x^2 + 144/x^2 = 40 (kalikan dengan x^2)
x^4 + 144 = 40x^2
(x^2)^2 - 40x^2 + 144 = 0. misal x^2 = a, maka
a^2 - 40a + 144 = 0
(a-4)(a-36) = 0
a = 4 atau a = 36
untuk a = 4, maka
x^2 = 4
x = -2 dan 2
untung a = 36, maka
x^2 = 36
x = -6 dan 6
x = -2 ==» y = 12/-2 = -6
x = 2 ==» y = 12/2 = 6
x = -6 ==» y = 12/-6 = -2
x = 6 ==» y = 12/6 = 2
HP = { (-6,-2),(-2,-6),(2,6), (6,2) }