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2021 Latvia TST
1.1
Simple algebra warm up
Simple algebra warm up
Source: Latvian TST 2021 Day 1 P1
March 12, 2021
algebra
Problem Statement
Given real numbers
x
,
y
,
z
,
a
x,y,z,a
x
,
y
,
z
,
a
satisfying:
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
Prove that at least one of the numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
is equal to
a
a
a
.
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