Question

Решите систему уравнений:
$\left \{ {{\frac{x}{y} +\frac{y}{x} =\frac{5}{2} \\} \atop {x+y=6}} \right.$

Answer 1

x/y + y/x = 5/2

x + y = 6

x/y = t   x,y≠0

y/x = 1/t

t + 1/t = 5/2

(t² + 1)/t  = 5/2

t² + 1 = 5/2 * t

2t² + 2 = 5t

2t² - 5t + 2 = 0

D= 25 - 16 = 9

t12=(5+-3)/4 =  1/2   2

1/ x/y = 1/2

y = 2x

x + 2x = 6

x = 2    y = 2x = 4

2/ x/y = 2

x = 2y

2y + y = 6

y = 2    x=2y = 4

ответ (4. 2)  (2. 4)