Question

Fun question.

Answer 1

find the number of integer solutions

\(\large \begin{align} \color{black}{\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{400}\hspace{.33em}\\~\\}\end{align}\)

Answer 2

@hartnn I was contributing to the question c;

Answer 3

\(\infty\) many ?

Answer 4

\(\large \begin{align} \color{black}{a.)86\\
b.) 89\\
c.) 90\\
d.)91\\
e.)44
\hspace{.33em}\\~\\}\end{align}\)

Answer 5

Here's a graph..

https://www.desmos.com/calculator/nd9az8pocy

I don't know how that's supposed to help but just throwing that out there..

Answer 6

This is a fun question. I've seen it before, so I won't spoil it. Although you should clarify: do we include duplicate solutions, i.e. if (x, y) is a solution, x !=y, do we also count (y, x) ?

HINT:\[ \frac{1}{x} + \frac{1}{y} = \frac{1}{n} \iff (x-n)(y-n) = n^2 \]

Answer 7

yes the hint is perfect!

Answer 8

example
\(x=720,y=900\)
and
\(x=900,y=720\)

yes so we count this \(\uparrow\) solutions, of which you are calling duplicate

Answer 9

Ah OK that makes sense. Because the answer I got didn't match of of yours, but I was making that assumption. Nobody else seems to be trying this question :(

I assume you know how to do it, and aren't asking for help?

Answer 10

iam

Answer 11

yes i know this , i m asking just for fun as stated.