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?