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Pythagorean Triples and Quadratic Coefficients : 'If a + b = 7, and a^2 + b^2 = 37, then what is the value of ab?'

1. If a + b = 7, and a2 + b2 = 37, then what is the value of ab?

2. Isn't there an easy way to find out Pythagorean Triplets?
3:4:5
6:8:10
5:12:13
8:15:17
7:24:25
Please provide an equation or easy way to get triplets- e.g. some kind of relation.
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Solution Summary

Pythagorean triples and quadratic coefficents are investigated. The solution is detailed and well presented.

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