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Iran MO (2nd Round)
1985 Iran MO (2nd round)
2
Find the value od the fraction - [Iran Second Round 1985]
Find the value od the fraction - [Iran Second Round 1985]
Source:
December 28, 2010
algebra proposed
algebra
Problem Statement
Let
x
,
y
x, y
x
,
y
and
z
z
z
be three positive real numbers for which
x
2
+
y
2
+
z
2
=
x
y
+
y
z
+
z
x
.
x^2+y^2+z^2=xy+yz+zx.
x
2
+
y
2
+
z
2
=
x
y
+
yz
+
z
x
.
Find the value of
x
x
+
y
+
z
.
\frac{\sqrt x}{\sqrt x + \sqrt y+ \sqrt z}.
x
+
y
+
z
x
.
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