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Poland - Second Round
1962 Poland - Second Round
1
1
Part of
1962 Poland - Second Round
Problems
(1)
x + y + z = a, 1/x +1/y +1/ z = 1/a
Source: Polish MO Second Round 1962 p1
8/31/2024
Prove that if the numbers
x
x
x
,
y
y
y
,
z
z
z
satisfy the equationw
x
+
y
+
z
=
a
,
x + y + z = a,
x
+
y
+
z
=
a
,
1
x
+
1
y
+
1
z
=
1
a
,
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{a},
x
1
+
y
1
+
z
1
=
a
1
,
then at least one of them is equal to
a
a
a
.
algebra
system of equations