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Canadian Mathematical Olympiad Qualification Repechage
2015 Canadian Mathematical Olympiad Qualification
5
((x + 1)/x)^2 + ((y + 1)/y)^2 >= 18
((x + 1)/x)^2 + ((y + 1)/y)^2 >= 18
Source: Canada Repêchage 2015/5
June 18, 2016
algebra
Inequality
inequalities
Problem Statement
Let
x
x
x
and
y
y
y
be positive real numbers such that
x
+
y
=
1
x + y = 1
x
+
y
=
1
. Show that
(
x
+
1
x
)
2
+
(
y
+
1
y
)
2
≥
18.
\left( \frac{x+1}{x} \right)^2 + \left( \frac{y+1}{y} \right)^2 \geq 18.
(
x
x
+
1
)
2
+
(
y
y
+
1
)
2
≥
18.
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