Question

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Answer 1

$\frac{x}{y} + \frac{y}{x} = a \\ x + y = 2a$

$\frac{x \times x}{xy} + \frac{y \times y}{xy} = \frac{axy}{xy}$

${x}^{2} + {y}^{2} = axy$

$x + y = 2a \: = > {(x + y)}^{2} = 4 {a}^{2}$

${x}^{2} + 2xy + {y}^{2} = 4 {a}^{2}$

${x}^{2} + {y}^{2} = 4 {a}^{2} - 2xy$

$= > 4 {a}^{2} - 2xy = axy$

$4 {a}^{2} = axy + 2xy$

$4 {a}^{2} = xy(a + 2)$

$= > xy = 4 \\ a + 2 = {a}^{2}$

$a = 2$

(x,y)= {(1,4),(2,2),(4,1)}