Question

X+Y=1
1/x=x/y
Решите систему уравнения.

Answer 1

х + у = 1, у = 1 - х, ⇒  1 - х = х², ⇒ х² +х -1 = 0 , ⇒х = (-1+-√5)/2
у = х²
у =( (-1+-√5)/2 )² = (1+-2√5 +5)/4 = (3+-√5)/2

Answer 2

x+y = 1
y = x^2

y = 1-x
y = x^2

x^2 = 1-x
x^2 + x - 1 = 0
D = 1 +4 = 5
x1 = (-1-√5)/2    y1 = 1 + (1+√5)/2 = (3+√5)/2
x2 = (-1+√5)/2    y2 = 1 + (1-√5)/2 = (3-√5)/2

Ответ: ((-1-√5)/2; (3+√5)/2); ((-1+√5)/2; (3-√5)/2)