Find a Pythagorean triplet in which one member is 28.

To find a Pythagorean triplet where one of the numbers is 28, we use the general formula for generating Pythagorean triplets:

• 2m
• m² - 1
• m² + 1

Here, m is a natural number greater than 1. We evaluate each possible case:

Case 1: When m2 + 1 = 28

Simplifying: m2 = 28 - 1
m2 = 27

Since 27 is not a perfect square, m will not be an integer. Hence, this case does not yield a valid Pythagorean triplet.

Case 2: When m2 - 1 = 28

Simplifying: m2 = 28 + 1
m2 = 29

Again, 29 is not a perfect square, so m will not be an integer. This case also does not result in a valid Pythagorean triplet.

Case 3: When 2m = 28

Simplifying: m = 28 / 2
m = 14

Here, m is a natural number greater than 1. We can now calculate the other two members of the Pythagorean triplet using the formulas:

• m2 - 1 = 142 - 1 = 196 - 1 = 195
• m2 + 1 = 142 + 1 = 196 + 1 = 197

Thus, the Pythagorean triplet is 28, 195, and 197.