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2014 SDMO (Middle School)
4
Sum of numbers and their reciprocals not both being zero
Sum of numbers and their reciprocals not both being zero
Source: 2014 SDMO Middle School Problem 4
August 28, 2016
Problem Statement
Let
a
a
a
,
b
b
b
, and
c
c
c
be nonzero real numbers. Prove that
a
+
b
+
c
a+b+c
a
+
b
+
c
and
1
a
+
1
b
+
1
c
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}
a
1
+
b
1
+
c
1
cannot both be
0
0
0
.
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