Question

Tentukan koordinat-koordinat titik potong antara garis x + y = 3 dan kurva x^2 - 3x + y^2 = 5

Answer 1

X + y = 3
y = 3 - x

x^2 - 3x + y^2 = 5
x^2 - 3x + (3 - x)^2 = 5
x^2 - 3x + x^2 - 6x + 9 - 5 = 0
2x^2 - 9x + 4 = 0
(2x - 1)(x - 4) = 0
x1 = 1/2 , x2 = 4

y = 3 - x
y1 = 3 - 1/2 = 5/2
y2 = 3 - 4 = -1

koordinat titik2 potong = (1/2, 5/2) dan (4, -1)