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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2023 All-Russian Olympiad Regional Round
11.9
11.9
Part of
2023 All-Russian Olympiad Regional Round
Problems
(1)
Weird but easy inequality with absolute values
Source: ARO Regional stage 2023 11.9
2/16/2023
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are non-zero reals, prove that
∣
b
a
−
b
c
∣
+
∣
c
a
−
c
b
∣
+
∣
b
c
+
1
∣
>
1
|\frac{b} {a}-\frac{b} {c}|+|\frac{c} {a}-\frac{c}{b}|+|bc+1|>1
∣
a
b
−
c
b
∣
+
∣
a
c
−
b
c
∣
+
∣
b
c
+
1∣
>
1
.
absolute value
algebra
Russia
inequalities proposed