Hello,
I need a little help in figuring this weird problem...
--we know that (2+3)^2 is not equal to 2^2 and 3^2...
however... (2+3)^2 = (2+1)^2 + (3+1)^2!
so determine, all values for m and n such that---
(m+n)^2 = (m+1)^2 + (n+1)^2
Thanks!
Hello,
I need a little help in figuring this weird problem...
--we know that (2+3)^2 is not equal to 2^2 and 3^2...
however... (2+3)^2 = (2+1)^2 + (3+1)^2!
so determine, all values for m and n such that---
(m+n)^2 = (m+1)^2 + (n+1)^2
Thanks!
$\displaystyle (m+n)^2 = (m+1)^2 + (n+1)^2$
expand & simplify results in
$\displaystyle mn = m+n+1 $
If the product of any two numbers is equal to the sum of the two numbers plus 1, then they work.
Is that what you had in mind?
2,3 is a solution that you have given.
It appears that is the only solution in natural numbers.
.
thanks for the response!
yeah I also simplified that and ended up getting (m-1)(n-1) = 2...that means m and n can only have 2 or 3 values respectively.
I was just making it too complicated..I thought it would be a little bit harder that it seems!
Hence, m =2 or 3 and n = 3 or 2...right?
Thanks a lot!