the-honk/challenges/euler/thoughts/9 - Special Pythagorean triplet.md

Proof

let x be the sum

LaTeX

c = x - (a + b) \\
a^2 + b^2 = (x - (a + b))^2 \\
a^2 + b^2 = a^2 + 2ab - 2ax + b^2 - 2bx + x^2 \\
2ab - 2ax - 2bx + x^2 = 0 \\
\\
2bx - 2ab = x^2 - 2ax \\
(\frac{x^2}{x}) - 2a = 2b - (\frac{2ab}{x}) \\
-2a = 2b - (\frac{2ab}{x}) - (\frac{x^2}{x}) \\
\\
a = \frac{2bx - x^2}{2x - 2b}