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Problems
Contests
National and Regional Contests
Turkey Contests
Akdeniz University MO
1997 Akdeniz University MO
2
2
Part of
1997 Akdeniz University MO
Problems
(2)
Very easy inequality
Source:
1/30/2016
If
x
x
x
and
y
y
y
are positive reals, prove that
x
2
x
y
+
y
2
y
x
≥
x
2
+
y
2
x^2\sqrt{\frac{x}{y}}+y^2\sqrt{\frac{y}{x}} \geq x^2+y^2
x
2
y
x
+
y
2
x
y
≥
x
2
+
y
2
inequalities
easy inequality
easy inequality
Source:
1/30/2016
Let
x
,
y
,
z
,
t
x,y,z,t
x
,
y
,
z
,
t
be real numbers such that,
1
≤
x
≤
y
≤
z
≤
t
≤
100
1 \leq x \leq y \leq z \leq t \leq 100
1
≤
x
≤
y
≤
z
≤
t
≤
100
. Find minimum value of
x
y
+
z
t
\frac{x}{y}+\frac{z}{t}
y
x
+
t
z
inequalities
algebra