A student is asked to calculate the Pythagorean Triples for the number 9 using the identity (x2 − y2)2 + (2xy)2 = (x2 + y2)2. The

A student is asked to calculate the Pythagorean Triples for the number 9 using the identity (x2 − y2)2 + (2xy)2 = (x2 + y2)2. The student's steps are shown below.

     Step 1: 9 = 5^2 − 4^2; therefore, x = 5 and y = 4

     Step 2: (5^2 − 4^2)2 + (2 ⋅ 5 ⋅ 4)^2 = (5^2 + 4^2)^2

     Step 3: (a − b)^2 + (40)^2 = (25 + 16)^2

     Step 4: (9)^2 + (40)^2 = (c)^2

     Step 5: The Pythagorean Triples are 9, 40, and 41.

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

 

 a.)5, 4, 41

B.) 9, 5, 41 

C.)9, 40, 41 

d.)25, 16, 41