Mathematics

Yusuf Short

19 August, 10:13

A student is asked to calculate the Pythagorean Triples for the number 15 using the identity (x2 - y2) 2 + (2xy) 2 = (x2 + y2) 2. The

student's steps are shown below.

Step 1: 15 = 82 - 72, therefore, x = 8 and y = 7

Step 2: (82 - 72) 2 + (2-8-7) 2 = (82 + 7272

Step 3: (a - b) 2 + (112) 2 = (54 + 49) 2

Step 4: (15) 2 + (112) 2 = (c) 2

Step 5: The Pythagorean Triples are 15, 112, and 113.

In Steps 3 and 4, what are the values of a, b, and c, respectively?