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Assam Mathematics Olympiad 2023 Category III Q4
Assam Mathematics Olympiad 2023 Category III Q4
Source:
September 11, 2024
Problem Statement
Real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
(
2
b
−
a
)
2
+
(
2
b
−
c
)
2
=
2
(
2
b
2
−
a
c
)
(2b - a)^2 + (2b - c)^2 = 2(2b^2 - ac)
(
2
b
−
a
)
2
+
(
2
b
−
c
)
2
=
2
(
2
b
2
−
a
c
)
. Prove that
a
+
c
=
2
b
a + c = 2b
a
+
c
=
2
b
.
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