A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) that satisfy the equation \(a^2 + b^2 = c^2\). Using \(x = 3\) and \(y = 6\) produces values \(3\) and \(6\) that do not form a valid relationship with any integer \(c\) since \(3^2 + 6^2 = 9 + 36 = 45\), which is not a perfect square.
In 1-2 sentences, explain why a Pythagorean triple cannot be created by using x=3
and y=6
. (2 points)
1 answer