Question

The number of positive integral solutions of $ta{n}^{-1}x+co{t}^{-1}y=ta{n}^{-1}3$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$ta{n}^{-1}\left(3\right)-ta{n}^{-1}\left(x\right)=ta{n}^{-1}\left(\frac{1}{y}\right)$
Hence
$\frac{1}{y}=\frac{3-x}{1+3x}$
$y=\frac{1+3x}{3-x}$
Now For positive integral solution, considering $x>0$ and x being an integer.
Hence let $x=1$, we get
$y=\frac{4}{2}$
$=2$
Hence we get our first positive integral solution as $(1,2)$.
Substituting, x=2, we get
$y=7$
Hence
$(1,2),(2,7)$
For x=3 , there is no definite solution, and for $x>3$, $y<0$
Hence there are only 2, positive integral solutions of the above equation.