Answer: Here i will explain it to you and give an example
Here's an example: let's say you have three positive integers, 5, 12, and 13. To check if they form a Pythagorean triple, you can compute 5^2 + 12^2 = 25 + 144 = 169, which is equal to 13^2. Since the equation holds, the three numbers 5, 12, and 13 form a Pythagorean triple.
In fact, this is a well-known Pythagorean triple, because it is one of the smallest triples, and it is frequently used in geometry and mathematics. The triple (5, 12, 13) satisfies the Pythagorean theorem and represents the lengths of the sides of a right triangle.
Step-by-step explanation: Three positive numbers form a Pythagorean triple if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words, if a, b, and c are the lengths of the sides of a triangle such that c is the length of the hypotenuse (the longest side) and a and b are the lengths of the other two sides, then the Pythagorean theorem states that a^2 + b^2 = c^2.
Therefore, to determine if three positive numbers form a Pythagorean triple, you need to check if the sum of the squares of the two smaller numbers is equal to the square of the largest number. For example, if you have three numbers 3, 4, and 5, you can check if they form a Pythagorean triple by computing 3^2 + 4^2 = 9 + 16 = 25, which is equal to 5^2. Since the equation holds, the numbers 3, 4, and 5 form a Pythagorean triple.
Hope this helped. Have a great day.