MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2024-25 IOQM India
5
IOQM P5 2024
IOQM P5 2024
Source:
September 8, 2024
Problem Statement
Let
a
=
x
y
+
y
z
+
z
x
a = \frac{x}{y} +\frac{y}{z} +\frac{z}{x}
a
=
y
x
+
z
y
+
x
z
, let
b
=
x
z
+
y
x
+
z
y
b = \frac{x}{z} +\frac{y}{x} +\frac{z}{y}
b
=
z
x
+
x
y
+
y
z
and let
c
=
(
x
y
+
y
z
)
(
y
z
+
z
x
)
(
z
x
+
x
y
)
c = \left(\frac{x}{y} +\frac{y}{z} \right)\left(\frac{y}{z} +\frac{z}{x} \right)\left(\frac{z}{x} +\frac{x}{y} \right)
c
=
(
y
x
+
z
y
)
(
z
y
+
x
z
)
(
x
z
+
y
x
)
. The value of
∣
a
b
−
c
∣
|ab-c|
∣
ab
−
c
∣
is:
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