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Problem
Problem
The three numbers
x
x
x
,
y
y
y
, and
z
z
z
are such that
x
>
y
>
z
>
0
x > y > z > 0
x
>
y
>
z
>
0
. Show that if
1
x
\frac{1}{x}
x
1
,
1
y
\frac{1}{y}
y
1
, and
1
z
\frac{1}{z}
z
1
are consecutive terms of an arithmetic sequence, then
x
−
z
x - z
x
−
z
,
y
y
y
, and
x
−
y
+
z
x - y + z
x
−
y
+
z
could be the lengths of the sides of a right angled triangle.
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