,![\[
\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}}
\]](http://latex.artofproblemsolving.com/e/7/2/e72fd0f134289c359bc8766440babc52ae131961.png)
satisfied 
Find the minimum of 
satisfy that: 
and natural number 
,
are there such that 
and 
?
and 
.
be real numbers such that 
Prove that
Let 
Prove that
and 
, then we can deduce 
\le 2 $ ?
satisfying 
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0 \le (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \le 164.
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Y by Adventure10
A rectangular sheet of paper was bent diagonally.
Can the perimeter the resulting pentagon turn out to be equal to the perimeter of the original sheet?
Can the perimeter the resulting pentagon turn out to be equal to the perimeter of the original sheet?
.
the short side and 
the long side of the rectangle and our objective is to solve for 
such that 
.
and the square root is always greater than 1.
,
