Final answer:
The Pythagorean triple generated by using 4 for x and 1 for y is 15, 8, 17, where 15 and 8 are the legs of the right triangle and 17 is the hypotenuse.
Step-by-step explanation:
The student has asked for the Pythagorean triple generated by using 4 for x and 1 for y. A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². These triples can be generated using the formulas: a = x² - y², b = 2xy, and c = x² + y², where x and y are positive integers with x > y.
Using 4 for x and 1 for y, we calculate the following:
- a = 4² - 1² = 16 - 1 = 15
- b = 2 × 4 × 1 = 8
- c = 4² + 1² = 16 + 1 = 17
Therefore, the Pythagorean triple generated is 15, 8, 17.