SOLUTION: Is the following set of numbers a perfect triple? 6, 8, 10

Question 286011: Is the following set of numbers a perfect triple? 6, 8, 10
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
If by perfect triple is meant Pythagorean triple, we must have the following criteria met (there are more but these should be more than sufficient...):
a^2+b^2=c^2
a=s^2-t^2
b=2st
c=s^2+t^2
with s,t integers. (Note: a and b are interchangeable, IE it doesn't matter which comes first in the first equation.) There are also interesting properties of s and t that one could investigate if interested.
Additionally, |a+b|<=|a|+|b|. IE the hypotenuse is less than or equal to the sum of the legs. This criteria is met by your three numbers, so we must investigate further with the first equation [easiest to do].
The question is: is 6^2+8^2=10^2?
IE is 36+64=100? Yes.
The last two lines are sufficient to understand the concept, but I hope you see there are many more relationships to note with Pythagorean triples than may be presented in a basic algebra or geometry text.

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