How to factorize x2-x-1

How to factorize x2-x-1

x²-x-1=（x-1/2）²-1/4-1
=（x-1/2）²-5/4
=（x-1/2）²-（√5/2）²
=（x-1/2+√5/2）（x-1/2-√5/2）

Solve the following equations (1) x2 / 4-y2 = 1, x-y-2 = 0: (2) (x-3) 2 + y2 = 9, x + 2Y = 0 (3) x2 + y2 = 4, x2-y2 = 2

（1)x=2 y=0 ; x=10/3 y=4/3
(2)x=0 y=0 ;x=24/5 y=-12/5
(3)x=√3 y=1 ;x=-√3 y=-1

Solve the following equations (1) x2 / 4-y2 = 1, x-y-2 = 0: (2) (x-3) 2 + y2 = 9, x + 2Y = 0

1. Changing x-y-2 = 0 into x = y + 2 into x2 / 4-y2 = 1, we can get 3y2-4y = 0, y = 0 or y = 4 / 3, x = 2 or x = 10 / 3
2 into y = - X / 2 to (x-3) 2 + y2 = 9, we get 5x2-24x = 0, x = 0; y = 0 or x = 24 / 5; y = - 12 / 5