A nice math Olympiad question| Solve for a+b=?
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Nice. Please explain the definition of a, b, and c in terms of n. Are they standard formulae for right-angled triangles in addition to Pythagorean theory? I mean the c=(n^2+1)/2; b=(n^2-1)/2 if the 3rd side is n. What is this formula called, please?
Thank you 😊. We can write in this way also c=n^2+1, b=n^2-1 and a=2n, you will see c^2=a^2+b^2. So this is right triangle or converse would be as I mentioned in video " if a, b, c are the sides of a right triangle (with a,b,c integer valued), c being the hypotenuse, then c=n^2+1, b=n^2-1 and a=2n
Yea, I don't know how/when it can be used. Can it be used for any Pythagorean triangle? If not, is there a certain insight that suggests it's use here? If 15 or 29 were the given value rather than 613 , would the approach be the same?
@@mks-learning-easy Your formula does NOT always work. If I take the classic 3, 4, 5 triangle, it works. However, the special 3,4,5 rule applies to any mulitple of those numbers (6, 8, 10.... 9, 12, 15... etc.) If I let n =9 and apply your fourmula, I would get b=40 and c=41. 9,40,41 IS a right triangle, but not the one I described. If I start with c=15, I would get a=SQRT(29), not 9 so I would not get an integer solution using your methodology even though one exists!