MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2016 ASDAN Math Tournament
14
2016 Team #14
2016 Team #14
Source:
August 17, 2022
2016
team test
Problem Statement
Suppose that
x
,
y
,
z
x,y,z
x
,
y
,
z
are positive real numbers that satisfy \begin{align*} x+y+z&=xyz\\ \frac{x^2}{16(1+x^2)}=\frac{y^2}{25(1+y^2)}&=\frac{z^2}{36(1+z^2)}. \end{align*} Compute
x
2
(
1
+
x
2
)
2
x
2
(
1
+
z
2
)
2
.
\frac{x^2(1+x^2)^2}{x^2(1+z^2)^2}.
x
2
(
1
+
z
2
)
2
x
2
(
1
+
x
2
)
2
.
Back to Problems
View on AoPS