Question

a^2 - ab - b^2
plz answer. ​

Answer 1

Answer:

worked something similar a few years back=perhaps you will find this relevant. a^2 +2ab +b^2 is a perfect square. It can always be written as (a+b)^2. The question I had (probably since algebra class), but never explored, was could a^2+ab+b^2 ever be a perfect square? i.e. a^2+ab+b^2=c^2 where a, b, and c are integers. I did find some solutions. I expect you could do the same for a^2-ab+b^2. In general, there are only a couple expressions like a^2+2ab+b^2 and a^2-b^2 that factor in such a simple manner. You can even do the same thing for a^2+b^2=c^2 and there are a number of solutions like the 3,4, 5 and 5,12, 13 right triangles. (You should recognize the Pythagoren theorem equation a^2+b^2=c^2 for this latter case.) And of course, any integral multiples of these solutions will also be solutions.

Source https://www.physicsforums.com/threads/how-to-solve-a-2-ab-b-2.868333/

Answer 2

Answer:

(a−b)(a2+ab+b2)=a3−b3

Formula:

(x−y)(x2+xy+y2)=x3−y3