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National and Regional Contests
China Contests
(China) National High School Mathematics League
2017 China Second Round Olympiad
10
China Second Round Olympiad 2017 Test 1 Q10
China Second Round Olympiad 2017 Test 1 Q10
Source: Sep 10, 2017
September 10, 2017
inequalities
China
BPSQ
inequalities proposed
Problem Statement
Let
x
1
,
x
2
,
x
3
≥
0
x_1,x_2,x_3\geq 0
x
1
,
x
2
,
x
3
≥
0
and
x
1
+
x
2
+
x
3
=
1
x_1+x_2+x_3=1
x
1
+
x
2
+
x
3
=
1
. Find the minimum value and the maximum value of
(
x
1
+
3
x
2
+
5
x
3
)
(
x
1
+
x
2
3
+
x
3
5
)
.
(x_1+3x_2+5x_3)\left(x_1+\frac{x_2}{3}+\frac{x_3}{5}\right).
(
x
1
+
3
x
2
+
5
x
3
)
(
x
1
+
3
x
2
+
5
x
3
)
.
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