Question

Решите систему уравнений (x+y)(x-y)=0 и 2x-y=1

Answer 1

Решение
Решите систему уравнений
 (x+y)(x-y)=0
 2x-y=1

x² - y² = 0
y = 2x - 1

y = 2x - 1
x² - (2x - 1)² = 0

x² - 4x² + 4x - 1 = 0
- 3x² + 4x - 1 = 0
3x² - 4x+ 1 = 0
D = 16 - 4*3*1 =4
x1 = (4 - 2)/6
x1 =1/3
x2 = (4 + 2)/6
x2 =1

x1 = 1/3
y1 = 2*(1/3) - 1
y1 = - 1/3

x2 = 1
y2 = 2*1 - 1
y2 = 1

Ответ: (1/3;- 1/3) ; (1; 1)