Answer the following parts about the triple (9,12,15). (a) show that (9, 12,15) is a pythagorean triple. (b) prove that neither (9, 12,15) nor (12,9,15) can be found by choosing a pair of integers x and y with x > y and computing (x² − y²,2xy, x² +y²). (hint: what are the possible values of x and y if 2xy =12? what about if 2xy = 9? ) (c) wouldn’t it be nice if all pythagorean triples were generated by (x² − y²,2xy, x² +y²)? research pythagorean triples on the internet to discover what is known to be true about generating all pythagorean triples using this formula.