Thank you so much! You just gave me the best present one can give: something I can teach my kids.
So the square of their difference is known, and the difference itself is the square root of its square -- up to an ambiguous overall sign.
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And once you know the sum and the difference of two numbers, the numbers themselves are easy to determine.
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The great thing about this approach is that it generalizes. One "completes the cube" in essentially the same way, to solve cubic equations.
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