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National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1982 Swedish Mathematical Competition
2
2
Part of
1982 Swedish Mathematical Competition
Problems
(1)
abc >= (a+b-c)(b+c-a)(c+a-b) for a,b,c>0
Source: 1982 Swedish Mathematical Competition p2
3/28/2021
Show that
a
b
c
≥
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
abc \geq (a+b-c)(b+c-a)(c+a-b)
ab
c
≥
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
for positive reals
a
a
a
,
b
b
b
,
c
c
c
.
algebra
inequalities