       greetings and a question!

• To: mathgroup at smc.vnet.net
• Subject: [mg83116] greetings and a question!
• From: dimitris <dimmechan at yahoo.com>
• Date: Sun, 11 Nov 2007 03:02:51 -0500 (EST)

```Hello to all of you!

Unfortunately, family, working and research issues
prevent me from participating to the forum as frequent
as I used to.

Anyway...

It is my first post since a long time so everybody be patient!

A student of mine came across the following
equation in a mathematical contest:

In:=
eq = x^2 + y^2 + (a + b)*x - (a - b)*y + a^2 + b^2 - a - b + 1==0;

(all variables are assumed real)

Of course for Mathematica the solution is rather trivial.

In:=
\$Version

Out=
"5.2 for Microsoft Windows (June 20, 2005)"

In:=
eq = x^2 + y^2 + (a + b)*x - (a - b)*y + a^2 + b^2 - a - b + 1==0;

In:=
Reduce[eq, {a, b, x, y}, Reals]
ToRules[%]
eq /. %

Out=
a == 1 && b == 1 && x == -1 && y == 0

Out=
{a -> 1, b -> 1, x -> -1, y -> 0}

Out=
True

Can somebody explain concisely the mathematica concept
behind this solution? In fact I would be much obliged if somebody
pointed me out how to obtain the result by hand. Also, by curiosity,
how Mathematica reaches the result?

Dimitris

```

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