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Sweden Contests
Swedish Mathematical Competition
1974 Swedish Mathematical Competition
5
5
Part of
1974 Swedish Mathematical Competition
Problems
(1)
x_1 + x_3 = 2t x_2 , x_2 + x_4 = 2t x_3 , x_3 + x_5=2t x_4
Source: 1974 Swedish Mathematical Competition p5
3/26/2021
Find the smallest positive real
t
t
t
such that
{
x
1
+
x
3
=
2
t
x
2
x
2
+
x
4
=
2
t
x
3
x
3
+
x
5
=
2
t
x
4
\left\{ \begin{array}{l} x_1 + x_3 = 2t x_2 \\ x_2 + x_4 = 2t x_3 \\ x_3 + x_5=2t x_4 \\ \end{array} \right.
⎩
⎨
⎧
x
1
+
x
3
=
2
t
x
2
x
2
+
x
4
=
2
t
x
3
x
3
+
x
5
=
2
t
x
4
has a solution
x
1
x_1
x
1
,
x
2
x_2
x
2
,
x
3
x_3
x
3
,
x
4
x_4
x
4
,
x
5
x_5
x
5
in non-negative reals, not all zero.
system of equations
System
algebra