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2022 Irish Math Olympiad
6
a+b+c =1, prove algebraic statement
a+b+c =1, prove algebraic statement
Source: IrMO 2022
May 9, 2022
Algebraic Manipulations
algebra
inequalities
Problem Statement
6. Suppose a, b, c are real numbers such that a + b + c = 1. Prove that
a
3
+
b
3
+
c
3
+
3
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
=
1.
a^3 + b^3 + c^3 + 3(1-a)(1-b)(1-c) = 1.
a
3
+
b
3
+
c
3
+
3
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
=
1.
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