The Product of two numbers is six times their sum and the sum of their squares is 325. What are the two numbers?

Question

Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.

Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.

What are the numbers?

Answer 1

15 and 10
15 and 10 are the two numbers
15 x 10=150
6(15+10)=150
and 15*15 + 10*10 =325