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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2017 China Second Round Olympiad
10
10
Part of
2017 China Second Round Olympiad
Problems
(1)
China Second Round Olympiad 2017 Test 1 Q10
Source: Sep 10, 2017
9/10/2017
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
)
.
inequalities
China
BPSQ
inequalities proposed