Question

Verify that:
a^2+b^2, a^2-b^2 and 2ab are the measures of the sides of a right angled triangle where a and b are any two real numbers(a>b)

Answer 1

In the right angled triangle shown, u^2 = v^2 + w^2 -------- (1)

Let u = a^2+b^2 ; v = a^2-b^2 ; w = 2ab

You can substitute for u, v and w in equation (1) and prove they form a right triangle.