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7
min of xy+yz+zx+1/x+2/y+5/z
min of xy+yz+zx+1/x+2/y+5/z
Source: Turkey TST 2022 P7 Day 3
March 13, 2022
inequalities
algebra
Problem Statement
What is the minimum value of the expression
x
y
+
y
z
+
z
x
+
1
x
+
2
y
+
5
z
xy+yz+zx+\frac 1x+\frac 2y+\frac 5z
x
y
+
yz
+
z
x
+
x
1
+
y
2
+
z
5
where
x
,
y
,
z
x, y, z
x
,
y
,
z
are positive real numbers?
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