MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
1992 Turkey Team Selection Test
3
Turkey TST 1992 - P3: x_1.x_2...x_(n+1) >= n^(n+1)
Turkey TST 1992 - P3: x_1.x_2...x_(n+1) >= n^(n+1)
Source:
March 13, 2011
inequalities
inequalities proposed
Problem Statement
x
1
,
x
2
,
⋯
,
x
n
+
1
x_1, x_2,\cdots,x_{n+1}
x
1
,
x
2
,
⋯
,
x
n
+
1
are posive real numbers satisfying the equation
1
1
+
x
1
+
1
1
+
x
2
+
⋯
+
1
1
+
x
n
+
1
=
1
\frac{1}{1+x_1} + \frac{1}{1+x_2} + \cdots + \frac{1}{1+x_{n+1}} =1
1
+
x
1
1
+
1
+
x
2
1
+
⋯
+
1
+
x
n
+
1
1
=
1
Prove that
x
1
x
2
⋯
x
n
+
1
≥
n
n
+
1
x_1x_2 \cdots x_{n+1} \geq n^{n+1}
x
1
x
2
⋯
x
n
+
1
≥
n
n
+
1
.
Back to Problems
View on AoPS