[tex] \frac{x}{y} + \frac{y}{x} = a \\ x + y = 2a[/tex]
[tex] \frac{x \times x}{xy} + \frac{y \times y}{xy} = \frac{axy}{xy} [/tex]
[tex] {x}^{2} + {y}^{2} = axy[/tex]
[tex]x + y = 2a \: = > {(x + y)}^{2} = 4 {a}^{2} [/tex]
[tex] {x}^{2} + 2xy + {y}^{2} = 4 {a}^{2} [/tex]
[tex] {x}^{2} + {y}^{2} = 4 {a}^{2} - 2xy[/tex]
[tex] = > 4 {a}^{2} - 2xy = axy[/tex]
[tex]4 {a}^{2} = axy + 2xy[/tex]
[tex]4 {a}^{2} = xy(a + 2)[/tex]
[tex] = > xy = 4 \\ a + 2 = {a}^{2} [/tex]
[tex]a = 2[/tex]
(x,y)= {(1,4),(2,2),(4,1)}
