Question

If $xy=2(x+y),x\le y$ and $x,y\in N$, then the number of solutions of the equation are

• A. two
• B. three
• C. no solution
• D. infinitely many solutions

Answer 1

The correct option is A two

Given, $xy=2(x+y)$

$\Rightarrow xy-2x=2y$

$\Rightarrow y=\frac{2x}{x-2}$
$x-2\ne 0\Rightarrow x\ne 2$
$x<y\Rightarrow x<\frac{2x}{x-2}\Rightarrow x(x-4)<0$
$\Rightarrow xϵ(0,4)\Rightarrow x=1,3$
So, number of solution is $2$.