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Czech-Polish-Slovak Match
2005 Czech-Polish-Slovak Match
1
1
Part of
2005 Czech-Polish-Slovak Match
Problems
(1)
Simultaneous equations in n variables
Source: Czech-Polish-Slovak 2005 Q1
4/27/2013
Let
n
n
n
be a given positive integer. Solve the system
x
1
+
x
2
2
+
x
3
3
+
⋯
+
x
n
n
=
n
,
x_1 + x_2^2 + x_3^3 + \cdots + x_n^n = n,
x
1
+
x
2
2
+
x
3
3
+
⋯
+
x
n
n
=
n
,
x
1
+
2
x
2
+
3
x
3
+
⋯
+
n
x
n
=
n
(
n
+
1
)
2
x_1 + 2x_2 + 3x_3 + \cdots + nx_n = \frac{n(n+1)}{2}
x
1
+
2
x
2
+
3
x
3
+
⋯
+
n
x
n
=
2
n
(
n
+
1
)
in the set of nonnegative real numbers.
algebra
polynomial
calculus
derivative
function
analytic geometry
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