The numbers $x$ and $y$ are positive integers where $x^2-xy=23$ . What is the value of $x+y$ ?

34
35
30
24
45

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Lol I sort of cheated by using the values from the options given, and a calculator.

What I did was:

Let x+y = k ....(1)

x^2 -xy=23

x- 23/x = y .....(2)

(1)+(2): 2x^2-kx-23=0 x=[k +/- sqrt(k^2+184)]/4

Since sqrt(k^2+184) > sqrt(k^2), thus consider only x=[k + sqrt(k^2+184)]/4, since k-sqrt(k^2+184)<0 because x +y=k>0 since both x and y are positive.

Now, using the values given in the options and a calculator, k=30, 24,35,34 gives an decimal number while k=45 gives an integer.

Since x and y are integers, k should be an integer, so the answer must be 45.