MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
1997 Iran MO (3rd Round)
4
4
Part of
1997 Iran MO (3rd Round)
Problems
(1)
\sqrt {x-1}+...
Source: Iran Third Round MO 1997, Exam 3, P4
10/18/2005
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be real numbers greater than
1
1
1
such that
1
x
+
1
y
+
1
z
=
2
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2
x
1
+
y
1
+
z
1
=
2
. Prove that
x
−
1
+
y
−
1
+
z
−
1
≤
x
+
y
+
z
.
\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}\leq \sqrt{x+y+z}.
x
−
1
+
y
−
1
+
z
−
1
≤
x
+
y
+
z
.
inequalities
Cauchy Inequality
inequalities proposed