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1990 IMO Longlists
24
24
Part of
1990 IMO Longlists
Problems
(1)
Find t s.t. system of equations have solution - ILL1990 HUN2
Source:
9/18/2010
Find the real number
t
t
t
, such that the following system of equations has a unique real solution
(
x
,
y
,
z
,
v
)
(x, y, z, v)
(
x
,
y
,
z
,
v
)
:
{
x
+
y
+
z
+
v
=
0
(
x
y
+
y
z
+
z
v
)
+
t
(
x
z
+
x
v
+
y
v
)
=
0
\left\{\begin{array}{cc}x+y+z+v=0\\ (xy + yz +zv)+t(xz+xv+yv)=0\end{array}\right.
{
x
+
y
+
z
+
v
=
0
(
x
y
+
yz
+
z
v
)
+
t
(
x
z
+
xv
+
y
v
)
=
0
quadratics
inequalities
algebra
system of equations
algebra proposed