Question

The two numbers x and y that satisfy $\left(xy\right),\left(\frac{x}{y}\right),(x+y)$ such that they are equal are

Answer 1

Given,

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

if

$\Rightarrow \frac{x}{y}=xy$

$\Rightarrow \frac{1}{y}=y$

$y^2=1$

$y=1or-1$ substituting $y=1inxy=x+y$

$\Rightarrow \text{x=x+1 but this is not possible as it will give 1=0}$

now substituting

$y=-1inxy=x+y$

$\Rightarrow -x=x-1$
$\Rightarrow 2x=1$

$\Rightarrow x=\frac{1}{2}$

so we have $y=-1andx=\frac{1}{2}$