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MathLinks Contest 5th
6.3
0563 inequalities 5th edition Round 6 p3
0563 inequalities 5th edition Round 6 p3
Source:
May 6, 2021
algebra
inequalities
5th edition
Problem Statement
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be three positive numbers such that
(
x
+
y
−
z
)
(
1
x
+
1
y
−
1
z
)
=
4
(x + y-z) \left( \frac{1}{x}+ \frac{1}{y}- \frac{1}{z} \right)=4
(
x
+
y
−
z
)
(
x
1
+
y
1
−
z
1
)
=
4
. Find the minimal value of the expression
E
(
x
,
y
,
z
)
=
(
x
4
+
y
4
+
z
4
)
(
1
x
4
+
1
y
4
+
1
z
4
)
.
E(x, y, z) = (x^4 + y^4 + z^4) \left( \frac{1}{x^4}+ \frac{1}{y^4}+ \frac{1}{z^4} \right) .
E
(
x
,
y
,
z
)
=
(
x
4
+
y
4
+
z
4
)
(
x
4
1
+
y
4
1
+
z
4
1
)
.
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