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Consider the equation 2/x+5/y=1/3w h e r...

Consider the equation `2/x+5/y=1/3w h e r ex ,y in Ndot` Find the number of solutions of the equation.

Text Solution

Verified by Experts

Given equation is `(2)/(x)+(5)/(y)=(1)/(3)`
or 6y+15x=xy
or `(x-6)(y-15)=90=2xx3^(2)xx5`
Consider (x-6) and (y-15) as boxes,
Number of solutions is same as number of ways 2,3,3,5 can be distributed in these boxes.
Number of ways 2 can be distributed =2
Number of ways 5 can be distributed =2
Number of ways (3,3) can be distributed =3
`therefore` Total number of solutions `=2xx2xx3=12`
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