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Question: How does Maple obtain this particular expression for the solution of the simple system x+y=2, x*y=4?

Question:How does Maple obtain this particular expression for the solution of the simple system x+y=2, x*y=4?

zenterix 405 Maple
solve explicit
December 05 2022
0

Consider the system of two equations 

x+y=2

x*y=4

Let's try to solve this using Maple's solve command.

This seems at first glance like one solution, but actually it is two, which I see if I use evalf.

Solving the equations by hand I get two solutions

y=1+sqrt(3)*i, x=4/y

y=1-sqrt(3)*i, x=4/y

If I use evalf on these two solutions I get the same result as the two solutions using solve.

My question is where does the expression y=2* RootOf(_Z^2-_Z+1) come from?

By hand, y seems to be the solution to y^2-2y+4=0.
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