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MathLinks Contest 2nd
2.1
0221 inequalities 2nd edition Round 2 p1
0221 inequalities 2nd edition Round 2 p1
Source:
May 10, 2021
inequalities
2nd edition
Problem Statement
Given are six reals
a
,
b
,
c
,
x
,
y
,
z
a, b, c, x, y, z
a
,
b
,
c
,
x
,
y
,
z
such that
(
a
+
b
+
c
)
(
x
+
y
+
z
)
=
3
(a + b + c)(x + y + z) = 3
(
a
+
b
+
c
)
(
x
+
y
+
z
)
=
3
and
(
a
2
+
b
2
+
c
2
)
(
x
2
+
y
2
+
z
2
)
=
4
(a^2 + b^2 + c^2)(x^2 + y^2 + z^2) = 4
(
a
2
+
b
2
+
c
2
)
(
x
2
+
y
2
+
z
2
)
=
4
. Prove that
a
x
+
b
y
+
c
z
≥
0
ax + by + cz \ge 0
a
x
+
b
y
+
cz
≥
0
.
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