Any set of positive integers that satisfies the equation asquaredplusbsquaredequalscsquared is a Pythagorean triple. Determine whether the set of numbers is a Pythagorean triple. 2 comma 6 comma 9

To determine whether a set of three numbers is a Pythagorean Triple, the equation a² + b² = c², where c is the largest number, must hold true.

Solving the Left-Hand Side (LHS)

Let's first solve the left-hand side of the equation, or a² + b². In the set of numbers given in the question, 2 and 6 are the smaller numbers. Plugging these values into the equation, we get:

2² + 6² = 4 + 36 = 40

Solving the Right-Hand Side (RHS)

Now, we will solve the right-hand side of the equation. The largest number in the set is 9.

9² = 81

Comparing the LHS and RHS

The value of the left-hand side is 40, while the value of the right-hand side is 81. Since 40 ≠ 81, then a² + b² ≠ c² and this set of numbers is not a Pythagorean Triple.