a + b + c = 1000, so what is abc?

a pythagorean triplet must make a < b < c

we know that:

![](assets/pythagoras.svg)

let x be the sum

![](assets/9.svg)

### LaTeX

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