MathDB
Problems
Contests
National and Regional Contests
China Contests
China Northern MO
2019 China Northern MO
6
2019 CNMO P6
2019 CNMO P6
Source: 2019 China North MO Problem 6
February 22, 2020
Problem Statement
For nonnegative real numbers
a
,
b
,
c
,
x
,
y
,
z
a,b,c,x,y,z
a
,
b
,
c
,
x
,
y
,
z
, if
a
+
b
+
c
=
x
+
y
+
z
=
1
a+b+c=x+y+z=1
a
+
b
+
c
=
x
+
y
+
z
=
1
, find the maximum value of
(
a
−
x
2
)
(
b
−
y
2
)
(
c
−
z
2
)
(a-x^2)(b-y^2)(c-z^2)
(
a
−
x
2
)
(
b
−
y
2
)
(
c
−
z
2
)
.
Back to Problems
View on AoPS