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Inequality transformed in an equation!
Inequality transformed in an equation!
Source:
February 4, 2015
inequalities
Problem Statement
Solve the following equation for
x
,
y
,
z
∈
N
x , y , z \in \mathbb{N}
x
,
y
,
z
∈
N
:
(
1
+
x
y
+
z
)
2
+
(
1
+
y
z
+
x
)
2
+
(
1
+
z
x
+
y
)
2
=
27
4
\left (1+ \frac{x}{y+z} \right )^2+\left (1+ \frac{y}{z+x} \right )^2+\left (1+ \frac{z}{x+y} \right )^2=\frac{27}{4}
(
1
+
y
+
z
x
)
2
+
(
1
+
z
+
x
y
)
2
+
(
1
+
x
+
y
z
)
2
=
4
27
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