Question

The difference between the squares of two numbers is aperiod twice the square of the first number increased by the square of the second number is 19. Find the numbers.

Answer 1

numbers are are x and y
x^2-y^2=5
3x^2+y^2=31
Add them
4x^2=36, the y^2 disappear
x^2=9
x=3 and -3
check both
x=3, y=2 or -2
x=-3, y=2 or -2
(3, 2) (3, -2) (-3, 2) (-3, -2)