Question

The Pythagorean triple (5, 12, 13) can't be generated from the identity (x? 1)2 + (2x)2 = (x2 + 1)

which has only one variable, because the length of the hypotenuse (13 units) and the length of the longer
of the other two legs (12 units) are not 2 units apart.
Find a two-variable identity by incorporating a second variable, y, into the single-variable identity. Note
that x > 1, x > y, and x and y are positive integers.
Select the correct answer.
5

Answer 1

9514 1404 393

Answer:

A. (x² -y²)² +(2xy)² = (x² +y²)²

Explanation:

As is often the case with problems like this, the correct answer (A) is the only answer that is actually a true equation.

Choices B, C, D are only true if x or y is zero--a violation of the given condition that they are positive integers.