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2011 Cuba MO
4
4
Part of
2011 Cuba MO
Problems
(1)
x_1 + 2x_2 + 3x_3 +...+ 24x_{24} - 439 <= (x^2_1+... + x^2_{24})/2 + 2011
Source: 2011 Cuba MO 2.4
9/17/2024
Let
x
1
,
x
2
,
.
.
.
,
x
24
x_1, x_2, ..., x_{24}
x
1
,
x
2
,
...
,
x
24
be real numbers. prove that
x
1
+
2
x
2
+
3
x
3
+
.
.
.
+
24
x
24
−
439
≤
x
1
2
+
x
2
2
+
.
.
.
+
x
24
2
2
+
2011.
x_1 + 2x_2 + 3x_3 +...+ 24x_{24} - 439 \le \frac{x^2_1+x^2_2+... + x^2_{24}}{2}+ 2011.
x
1
+
2
x
2
+
3
x
3
+
...
+
24
x
24
−
439
≤
2
x
1
2
+
x
2
2
+
...
+
x
24
2
+
2011.
algebra
inequalities