How would I start off this question?

EddyBenzen122

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for some real numbers and n, the list 3n2 m2 2(n + 1)2 consists of three consecutive integers written in increasing order. determine all possible values of m.

I have no idea how I can start this equation and so I couldn't show any work. Would you mind helping me by giving me hints or whatever?
 
did you mean real numbers m and n, with the sequence

3n2,m2,2(n+1)23n^2, \, m^2, \, 2(n+1)^2 ???

if so, note the last term, 2(n+1)22(n+1)^2, is an even number (why?)

see what you can do from here
 
for some real numbers and n, the list 3n2 m2 2(n + 1)2 consists of three consecutive integers written in increasing order. determine all possible values of m.

I have no idea how I can start this equation and so I couldn't show any work. Would you mind helping me by giving me hints or whatever?
You were told that they are increasing consecutive integers so:
m23n2=1(eq 1)\tag{eq 1} m^2-3n^2=12(n+1)2m2=1(eq 2)\tag{eq 2} 2(n+1)^2-m^2=1It's a system of 2 equations and 2 unknowns. Solve for m,nm,\,n simultaneously.
 
2(n+1)23n2=22(n+1)^2-3n^2=2

(Finally, note there are 4 answers for m).
 
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