SOLUTION: show that (m^2-n^2, 2mn, m^2+n^2) is a phythagoream triple

Algebra ->  Pythagorean-theorem -> SOLUTION: show that (m^2-n^2, 2mn, m^2+n^2) is a phythagoream triple      Log On


   

Question 619109: show that (m^2-n^2, 2mn, m^2+n^2) is a phythagoream triple
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Those three expressions form a Pythagorean triple if and only if

(we can show that m^2 + n^2 > 2mn by the AM-GM inequality, m^2 + n^2 > m^2 - n^2 is obvious, given that m,n > 0).

Here, just show that LHS equal the RHS.



This is true, so the three expressions form a Pythagorean triple.