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Inequality with 1/x +1/y +1/z = 2
Inequality with 1/x +1/y +1/z = 2
Source:
September 1, 2010
inequalities
trigonometry
three variable inequality
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IMO Longlist
Problem Statement
Prove that if
x
,
y
,
z
>
1
x,y,z >1
x
,
y
,
z
>
1
and
1
x
+
1
y
+
1
z
=
2
\frac 1x +\frac 1y +\frac 1z = 2
x
1
+
y
1
+
z
1
=
2
, then
x
+
y
+
z
≥
x
−
1
+
y
−
1
+
z
−
1
.
\sqrt{x+y+z} \geq \sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.
x
+
y
+
z
≥
x
−
1
+
y
−
1
+
z
−
1
.
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