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