Solution

194721

First name
Joshua
School
Bohunt Sixth Form
Country
Age
0

not sure what happened in the last photo, here's what it says:
'So (NM)^2 + (AM)^2 = (AN)^2 is 1^2 + (sqrt(1/2))^2 = (sqrt(3/2))^2 or 1 + 1/2 = 3/2 which is true so this means if B is true (always) then A is true.
Sorry for bad diagrams too :)