Question

x^2+y^2=41
xy=20
решите систему кв.уравнений,пожалуйста)

Answer 1

x*2 + y*2 +2xy-2xy=41
(x+y)*2 = 41+2xy
(x+y)*2 = 41+40
(x+y)*2 = 81
x+y = 9
x=9-y
(9-y)y=20
y*2 - 9y + 20 = 0
(y - 9/2)*2 = -20 + 81/4
(y-9/2)*2 = 1/4
y-9/2 = 1/2
y = 1/2 + 9/2
y = 5
x = 9-5 =4