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All-Russian Olympiad Regional Round
1993 All-Russian Olympiad Regional Round
9.1
a^2 +ab+b^2>= 3(a+b-1).All-Russian MO 1993 Regional (R4) 9.1
a^2 +ab+b^2>= 3(a+b-1).All-Russian MO 1993 Regional (R4) 9.1
Source:
August 26, 2024
algebra
inequalities
Problem Statement
If
a
a
a
and
b
b
b
are positive numbers, prove the inequality
a
2
+
a
b
+
b
2
≥
3
(
a
+
b
−
1
)
.
a^2 +ab+b^2\ge 3(a+b-1).
a
2
+
ab
+
b
2
≥
3
(
a
+
b
−
1
)
.
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