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Finnish National High School Mathematics Competition
2014 Finnish National High School Mathematics
1
x^2+y^2+z^2 if x+y+z=13, xyz= 72, 1/x+1/y+1/z=3/4
x^2+y^2+z^2 if x+y+z=13, xyz= 72, 1/x+1/y+1/z=3/4
Source: Finland 2014, Problem 1
September 1, 2019
algebra
system of equations
Problem Statement
Determine the value of the expression
x
2
+
y
2
+
z
2
x^2 + y^2 + z^2
x
2
+
y
2
+
z
2
, if
x
+
y
+
z
=
13
x + y + z = 13
x
+
y
+
z
=
13
,
x
y
z
=
72
xyz= 72
x
yz
=
72
and
1
x
+
1
y
+
1
z
=
3
4
\frac1x + \frac1y + \frac1z = \frac34
x
1
+
y
1
+
z
1
=
4
3
.
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