Given two real numbers and , if is their sum and their product, and are:
This is basically the quadratic formula – note that .
Derivation using quadratic formula
and , so:
Since and are symmetrical in and , the same equation gives .
The difference in area between the red square and the largest square is evidently equal to 4 of the green rectangles each of area . (See in the right picture that the dark green overlap is equal in area to the square at top right not covered.)
Since similarly , and , the RHS also gives .
Pic from E. Hairer and G. Wanner, Analysis by its History, 2008.
Graph of and :