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National and Regional Contests
India Contests
India National Olympiad
1991 India National Olympiad
7
Solve this system
Solve this system
Source: INMO 1991 Problem 7
October 3, 2005
quadratics
complex numbers
algebra
system of equations
polynomial
Rational Root Theorem
Problem Statement
Solve the following system for real
x
,
y
,
z
x,y,z
x
,
y
,
z
{
x
+
y
−
z
=
4
x
2
−
y
2
+
z
2
=
−
4
x
y
z
=
6.
\{ \begin{array}{ccc} x+ y -z & =& 4 \\ x^2 - y^2 + z^2 & = & -4 \\ xyz & =& 6. \end{array}
{
x
+
y
−
z
x
2
−
y
2
+
z
2
x
yz
=
=
=
4
−
4
6.
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