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ISI B.Math Entrance Exam
2008 ISI B.Math Entrance Exam
9
B.Math 2008-System of equations
B.Math 2008-System of equations
Source: 10+2
April 16, 2012
algebra proposed
algebra
Problem Statement
For
n
≥
3
n\geq 3
n
≥
3
, determine all real solutions of the system of n equations :
x
1
+
x
2
+
.
.
.
+
x
n
−
1
=
1
x
n
x_1+x_2+...+x_{n-1}=\frac{1}{x_n}
x
1
+
x
2
+
...
+
x
n
−
1
=
x
n
1
.......................
x
1
+
x
2
+
.
.
.
+
x
i
−
1
+
x
i
+
1
+
.
.
.
+
x
n
=
1
x
i
x_1+x_2+...+x_{i-1}+x_{i+1}+...+x_n=\frac{1}{x_i}
x
1
+
x
2
+
...
+
x
i
−
1
+
x
i
+
1
+
...
+
x
n
=
x
i
1
.......................
x
2
+
.
.
.
+
x
n
−
1
+
x
n
=
1
x
1
x_2+...+x_{n-1}+x_n=\frac{1}{x_1}
x
2
+
...
+
x
n
−
1
+
x
n
=
x
1
1
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