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All-Russian Olympiad
1975 All Soviet Union Mathematical Olympiad
212
ASU 212 All Soviet Union MO 1975 a^3+b^3+c^3+3abc>ab(a+b)+bc(b+c)+ac(a+c)
ASU 212 All Soviet Union MO 1975 a^3+b^3+c^3+3abc>ab(a+b)+bc(b+c)+ac(a+c)
Source:
July 5, 2019
inequalities
algebra
Problem Statement
Prove that for all the positive numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
the following inequality is valid:
a
3
+
b
3
+
c
3
+
3
a
b
c
>
a
b
(
a
+
b
)
+
b
c
(
b
+
c
)
+
a
c
(
a
+
c
)
a^3+b^3+c^3+3abc>ab(a+b)+bc(b+c)+ac(a+c)
a
3
+
b
3
+
c
3
+
3
ab
c
>
ab
(
a
+
b
)
+
b
c
(
b
+
c
)
+
a
c
(
a
+
c
)
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