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

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

For this problem, I tried to tackle with factoring: a2+b2 = (a + b) 2
and then I plugged in 7 but this seems like a wrong way to approach. If
it is please explain why it is not a correct approach.

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.