# Thread: A number puzzle for u

1. ## A number puzzle for u

There are two numbers with the difference of 3 between them and the difference of their squares is 51.
Can you find the numbers???

2. Spoiler:
Suppose the two numbers are $\displaystyle a$ and $\displaystyle b$, with $\displaystyle a<b$.

Then the problem says that $\displaystyle b-a=3$ and $\displaystyle b^2-a^2=51$. Note that $\displaystyle b^2-a^2=(b-a)(b+a)$. Can you finish now?

3. Originally Posted by Bruno J.
Suppose the two numbers are $\displaystyle a$ and $\displaystyle b$, with $\displaystyle a<b$.

Then the problem says that $\displaystyle b-a=3$ and $\displaystyle b^2-a^2=51$. Note that $\displaystyle b^2-a^2=(b-a)(b+a)$. Can you finish now?
I suspect the OP was meant to be a challenge question (which is why the thread was moved to here and why I put spoiler tags around your reply).

4. @ Bruno: yes you are right,,,

5. Originally Posted by mr fantastic
I suspect the OP was meant to be a challenge question (which is why the thread was moved to here and why I put spoiler tags around your reply).
Then why post his solution immediately below?

6. X = 10
y = 7

7. Originally Posted by HallsofIvy
Then why post his solution immediately below?
I didn't want to delete the reply on the one hand but I didn't want the reply to be in plain sight on the other hand. So my third hand decided a good compromise would be to put spoiler tags around it.

8. Originally Posted by mr fantastic
So my third hand decided a good compromise would be to put spoiler tags around it.
Is 3 hands what makes you "fantastic"?