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All-Russian Olympiad
2019 All-Russian Olympiad
8
2019 All Russian MO Grade 9 P8
2019 All Russian MO Grade 9 P8
Source:
May 1, 2019
algebra
inequalities
Russia
High school olympiad
Problem Statement
For
a
,
b
,
c
a,b,c
a
,
b
,
c
be real numbers greater than
1
1
1
, prove that
a
+
b
+
c
4
≥
a
b
−
1
b
+
c
+
b
c
−
1
c
+
a
+
c
a
−
1
a
+
b
.
\frac{a+b+c}{4} \geq \frac{\sqrt{ab-1}}{b+c}+\frac{\sqrt{bc-1}}{c+a}+\frac{\sqrt{ca-1}}{a+b}.
4
a
+
b
+
c
≥
b
+
c
ab
−
1
+
c
+
a
b
c
−
1
+
a
+
b
c
a
−
1
.
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