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2016 Chandigarh RMO 1/a + 1/b +1/c<1 =>1/a + 1/b +1/c<= 41/42
2016 Chandigarh RMO 1/a + 1/b +1/c<1 =>1/a + 1/b +1/c<= 41/42
Source:
August 9, 2019
inequalities
algebra
Problem Statement
Positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
1
a
+
1
b
+
1
c
<
1
\frac1a +\frac1b +\frac1c<1
a
1
+
b
1
+
c
1
<
1
. Prove that
1
a
+
1
b
+
1
c
≤
41
42
\frac1a +\frac1b +\frac1c\le \frac{41}{42}
a
1
+
b
1
+
c
1
≤
42
41
. Also prove that equality in fact holds in the second inequality.
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