If the difference between two numbers is 7 and their product is 137 what is the sum of squares of the numbers

x-y = 7 …(1)

xy = 137 …(2)

Square (1) to get x^2 +y^2 - 2xy = 49, or

x^2 +y^2 = 2xy + 49 = 2*137 + 49 = 323 + 49 = 372.

The sum of the squares of the two numbers is 372.

The square of the sum of the two number: (x+y)^2 = x^2+2xy+y^2 = x^2 +y^2 - 2xy + 4 xy = 49 +4*137 = 49+548 = 597.