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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2022 China Second Round A1
1
find the maximum and minimum
find the maximum and minimum
Source: 2022 China Second Round A1 P1
October 30, 2022
maximum and minimum
inequalities
Problem Statement
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are real numbers so that
a
≥
b
,
c
≥
d
a\geq b,c\geq d
a
≥
b
,
c
≥
d
,
∣
a
∣
+
2
∣
b
∣
+
3
∣
c
∣
+
4
∣
d
∣
=
1.
|a|+2|b|+3|c|+4|d|=1.
∣
a
∣
+
2∣
b
∣
+
3∣
c
∣
+
4∣
d
∣
=
1.
Let
P
=
(
a
−
b
)
(
b
−
c
)
(
c
−
d
)
P=(a-b)(b-c)(c-d)
P
=
(
a
−
b
)
(
b
−
c
)
(
c
−
d
)
,find the maximum and minimum value of
P
P
P
.
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