2014 · Q67
Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units?
- a(2n + 1, 4n, 2n^2 + 2n)
- b(2n, 4n, n^2 + 1)
- c(2n^2, 2n, 2n + 1)
- d(2n, n^2 - 1, n^2 + 1) where n is a positive real number.
Elementary MathematicsGeometry
- A(2n + 1, 4n, 2n^2 + 2n)
- B(2n, 4n, n^2 + 1)
- C(2n^2, 2n, 2n + 1)
- D(2n, n^2 - 1, n^2 + 1)
Explanation
(2n)^2 + (n^2-1)^2 = (n^2+1)^2 and (n^2+1) - (n^2-1) = 2.