and 
Prove that
'is a perfect square.
and 
be positive real numbers with 
.
For which 
such that 
for all 
,
.
and 
of an equilateral triangle 
are taken points 
and 
,
, points 
and 
so that 
.
and 
is equal to 
.
over 
.
![\[\lfloor x \rfloor\]](http://latex.artofproblemsolving.com/d/3/f/d3f8facf62413e1f17c89b9c183a8735c2defe8b.png)
denote the greatest integer less than or equal to x . What is the sum of the squares of the real numbers x for which ![\[ x^2 - 20\lfloor x \rfloor + 19 = 0 \]](http://latex.artofproblemsolving.com/f/a/9/fa96f2d6217a16029e5f03499e0a83deffdfa28a.png)
Prove that
of the pizza, where 
is a positive integer. Find 
Y by Adventure10, Mango247
Let 
be a rectangle with sides 
and 
. Let 
be the intersection point of it's diagonals. Extent side 
towards 
at a segment 
, and diagonal 
towards 
at a segment 
. If the triangle 
is an equilateral, then prove that:
i)
ii)
iii)
be a rectangle with sides 
and 
. Let 
be the intersection point of it's diagonals. Extent side 
towards 
at a segment 
, and diagonal 
towards 
at a segment 
. If the triangle 
is an equilateral, then prove that:i)
ii)
iii)
