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1996 Tournament Of Towns
(488) 1
TOT 488 1996 Spring J A1 a^2 + b^2 - ab = c^2
TOT 488 1996 Spring J A1 a^2 + b^2 - ab = c^2
Source:
August 16, 2024
inequalities
algebra
Problem Statement
Prove that if
a
,
b
a, b
a
,
b
and
c
c
c
are positive numbers such that
a
2
+
b
2
−
a
b
=
c
2
,
a^2 + b^2 - ab = c^2,
a
2
+
b
2
−
ab
=
c
2
,
then
(
a
−
c
)
(
b
−
c
)
<
0.
(a - c)(b - c) < 0.
(
a
−
c
)
(
b
−
c
)
<
0.
(A Egorov)
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