Question

Решите систему уравнений {х-у=4 х²+у²=10

Answer 1

Х = 4 +у
х2 + у2 = 10

(4+у)2 + у2 = 10

16 + 8у + у2 + у2= 10
16 + 8у + 2у2 - 10 = 0
2у2 + 8у + 6 = 0  /:2
у2 + 4у + 3 = 0 
Д= 16 - 12 = 4 = 2
у1= 4 - 3 =1
у2= 4 - 1 = 3

Answer 2

X - y = 4
X^2 + y^2 = 10
Решение
у = Х - 4
Х^2 + ( Х - 4 )^2 = 10
Х^2 + х^2 - 8х + 16 - 10 = 0
2х^2 - 8х + 6 = 0
2( х^2 - 4х + 3 ) = 0
D = 16 - 12 = 4 = 2^2
X1 = ( 4 + 2 ) : 2 = 3
X2 = ( 4 - 2 ) : 2 = 1
y1 = 3 - 4 = - 1
y2 = 1 - 4 = - 3
Ответ ( 3 ; - 1 ) ; ( 1 ; - 3 )