SOLUTION: what is the only pair of consectutive integer whose square roots are also consecutive integer

Algebra ->  Test  -> Lessons -> SOLUTION: what is the only pair of consectutive integer whose square roots are also consecutive integer       Log On


   

Question 219182: what is the only pair of consectutive integer whose square roots are also consecutive integer



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the 1st integer
Then n+%2B+1 will be the 2nd integer
given:
sqrt%28n%29+=+m
sqrt%28n%2B1%29+=+m%2B1
Square both sides of both equations
(1)n+=+m%5E2
n+%2B+1+=+%28m%2B1%29%5E2
(2)n+%2B+1+=+m%5E2+%2B+2m+%2B+1
Substitute (1) in (2)
m%5E2+%2B+1+=+m%5E2+%2B+2m+%2B+1
1+=+2m+%2B+1
2m+=+0
m+=+0
n+=+m%5E2
n+=+0
n%2B1+=+1
The numbers are 0 and 1