MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAMO
2001 USAMO
3
3
Part of
2001 USAMO
Problems
(1)
Inequality with a^2+b^2+c^2+abc=4
Source: USAMO 2001 #3
6/27/2004
Let
a
,
b
,
c
≥
0
a, b, c \geq 0
a
,
b
,
c
≥
0
and satisfy
a
2
+
b
2
+
c
2
+
a
b
c
=
4.
a^2+b^2+c^2 +abc = 4 .
a
2
+
b
2
+
c
2
+
ab
c
=
4.
Show that
0
≤
a
b
+
b
c
+
c
a
−
a
b
c
≤
2.
0 \le ab + bc + ca - abc \leq 2.
0
≤
ab
+
b
c
+
c
a
−
ab
c
≤
2.
inequalities
symmetry
trigonometry
AMC
USA(J)MO
USAMO
quadratics