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International Olympiad of Metropolises
2020 IOM
4
Algebra IOM
Algebra IOM
Source: International Olympiad of metropolises problem 4
December 19, 2020
algebra
Problem Statement
Given three positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
such that following holds
a
2
=
b
2
+
b
c
a^2=b^2+bc
a
2
=
b
2
+
b
c
,
b
2
=
c
2
+
a
c
b^2=c^2+ac
b
2
=
c
2
+
a
c
Prove that
1
c
=
1
a
+
1
b
\frac{1}{c}=\frac{1}{a}+\frac{1}{b}
c
1
=
a
1
+
b
1
.
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