The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.

Answer 1

We are given
x²+y²=137

(x-y)=7
this means
49=(x-y)²
=x²-2xy+y²
=x²+y²-2xy
=137-2xy
From
49=137-2xy
can you solve for xy?

The longer way:
equation 1:
x-y=7
equation 2:
x²+y²=137

Now solve the non-linear system in x and y.