Question

Please help!!!. I don't know how to do it.

Find the values of x and y that produce the following Pythagorean triples:

39, 760, 761

Answer 1

39 has factors (1 * 39) & (3 * 13)
Here we'll try
m + n = 13
m - n = 3

2m = 16
m = 8

2n = 10
n = 5
2mn = 2 * 8 * 5 = 80
So this choice is no good.
Let's go with
m + n = 39
m - n = 1

2m = 40
m = 20

2n = 38
n = 19

Thus
x = 20² - 19² = 39
y = 2 * 20 * 19 = 760
z = 20² + 19² = 761