Question

demontrer le resultat suivant " la difference des carres de deux nombres entiers consecutifs est egale a la somme de ces deux nombres "

Answer 1

     Since they are consecutive, meaning that one is another added to a unit.

$a=b+1$
 
     Where: a>b

     Now, we must mathematizing the problem:

$a^2-b^2=a+b \\ (a+b)(a-b)=(a+b) \\ a-b=1 \\ \boxed {a=b+1}$
 
     Note that, the result was expected because we made "a^2-b^2" in order to give a positive number, since "a" and "b" are positive, then the sum of both should also give a positive number.

If you notice any mistake in English, please let me know, because I'm not native.