MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2018-IMOC
A5
(x^2+3)(y^2+3)(z^2+3)>=(xyz+x+y+z+4)^2 over R
(x^2+3)(y^2+3)(z^2+3)>=(xyz+x+y+z+4)^2 over R
Source: IMOC 2018 A5
August 15, 2021
inequalities
Problem Statement
Show that for all reals
x
,
y
,
z
x,y,z
x
,
y
,
z
, we have
(
x
2
+
3
)
(
y
2
+
3
)
(
z
2
+
3
)
≥
(
x
y
z
+
x
+
y
+
z
+
4
)
2
.
\left(x^2+3\right)\left(y^2+3\right)\left(z^2+3\right)\ge(xyz+x+y+z+4)^2.
(
x
2
+
3
)
(
y
2
+
3
)
(
z
2
+
3
)
≥
(
x
yz
+
x
+
y
+
z
+
4
)
2
.
Back to Problems
View on AoPS