To generate a Pythagorean triple using the polynomial identity, we can use the identity related to generating such triples, which is typically given by:
- \( a = x^2 - y^2 \)
- \( b = 2xy \)
- \( c = x^2 + y^2 \)
Given \( x = 8 \) and \( y = 5 \), we can calculate:
- \( a = 8^2 - 5^2 = 64 - 25 = 39 \)
- \( b = 2 \cdot 8 \cdot 5 = 80 \)
- \( c = 8^2 + 5^2 = 64 + 25 = 89 \)
So the Pythagorean triple is \( 39, 80, 89 \).
In ascending order, the answer is:
39,80,89