SOLUTION: The sum of the squares of two numbers is 1130 while the square of their sum is 1849. Find the two numbers.

Let x and y be these two numbers. Then

 = 1130,      (1)
 = 1849.      (2)

From (2), x + y = +/- = +/-43.

Now the original system (1),(2) deploys in two systems that should be solved separately.



1)  = 1130,      (1')
   x + y     = 43.      (2')

From (2'), express x via y as x = 43-y. Then substitute it into (1'). You will get

    = 1130.

Simplify and solve it. Can you do it on your own?



2)  = 1130,      (1'')
   x + y     = -43.     (2'')

From (2''), express x via y as x = -43-y. Then substitute it into (1''). You will get

    = 1130.

Simplify and solve it. Can you do it on your own?