30 points !
find the values of x and y that produce the following pythagorean triples :
1.) 65, 72, 97
2.) 25, 312, 313
3.) 39, 760, 761

show work if you can!

Let and be two legs of a right triangle. By Pythagoras' theorem, the hypotenuse will have length :



What you should do is read the first two values in the given lists as and , and the third as .

So for example, if I gave you the list 3, 4, 5, we take





Since , it follows that (3, 4, 5) is indeed a Pythagorean triple.

Let's check with the first problem: If and , we have



which means (65, 72, 97) is also a Pythagorean triple.