Question

A triangle is right angled if the sides are a=m2-n2, b=2mn and c= m2 + n2 where m and n are positive integers and m is greater then n.

show that this is true by substituting into the equation c2=a2+b2

Answer 1

Recall the algebra equation: (a+/-b)²=a²+/-2ab+b²)

a²+b²=(m²-n²)²+(2mn)²=(m²)²-2m²n²+(n²)²+2m²n²
=(m²)²+2m²n²+(n²)²=(m²+n²)²=c²