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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2018 Dutch BxMO TST
5
nx^2 +2^2/(x + 1}+...+(n + 1)^2/(x + n)= nx + n(n+3)/2
nx^2 +2^2/(x + 1}+...+(n + 1)^2/(x + n)= nx + n(n+3)/2
Source: Dutch BxMO TST 2018 p5
August 24, 2019
algebra
equation
Problem Statement
Let
n
n
n
be a positive integer. Determine all positive real numbers
x
x
x
satisfying
n
x
2
+
2
2
x
+
1
+
3
2
x
+
2
+
.
.
.
+
(
n
+
1
)
2
x
+
n
=
n
x
+
n
(
n
+
3
)
2
nx^2 +\frac{2^2}{x + 1}+\frac{3^2}{x + 2}+...+\frac{(n + 1)^2}{x + n}= nx + \frac{n(n + 3)}{2}
n
x
2
+
x
+
1
2
2
+
x
+
2
3
2
+
...
+
x
+
n
(
n
+
1
)
2
=
n
x
+
2
n
(
n
+
3
)
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