Answer:
x=2000
Step-by-step explanation:
The conditions state, being x, N, M positive integers:
[tex]x-64=N^2[/tex] [1]
[tex]x+25=M^2[/tex] [2]
Subtracting the [1] from [2]
[tex]89=M^2-N^2=(M-N)(M+N)[/tex]
Since 89 has no other prime factors except 1 and itself, we can write
[tex](M-N)(M+N)=(1)(89)[/tex]
[tex]M+N=89[/tex]
[tex]M-N=1[/tex]
This system of equations results in [tex]M=45, N=44[/tex]
Replacing in [1] or [2] results
[tex]x=2000[/tex]
Proof:
[tex]2000-64=1936 =44^2[/tex]
[tex]2000+25=2025=45^2[/tex]
