is polynomial with minimum degree such that 
for 
, find 
such that 
.
Prove that :
Where 
and 
such that 
and 
by either 
or 
.
be non-negative real numbers such that 
.![\[
P = \frac{a}{a^2 + 2} + \frac{b}{b^2 + 2} + \frac{c}{c^2 + 2}.
\]](http://latex.artofproblemsolving.com/d/b/e/dbea7db769c4996fc081ee75837e177b298cffcb.png)
be reals such that 
. Prove that
Let 
. Prove that
be a permutation of 
such that there are exactly 
ordered pairs of integers 
satisfying 
and 
.
and 
.
Y by Adventure10, Mango247
Given two points in a plane and a straightedge whose length is less than the distance between them (but no compass!), construct the line passing through the two points.
You may want to use a special case of Desargues' theorem:
Suppose we have two triangles,
and 
positioned in such a way that 
, and 
intersect in a point. Let lines 
and 
meet at point 
, lines 
and 
, meet at 
, and 
and 
at 
. Then, points 
, and are collinear (fig. ).
You may want to use a special case of Desargues' theorem:
Suppose we have two triangles,
and 
positioned in such a way that 
, and 
intersect in a point. Let lines 
and 
meet at point 
, lines 
and 
, meet at 
, and 
and 
at 
. Then, points 
, and are collinear (fig. ).
This post has been edited 1 time. Last edited by parmenides51, Aug 21, 2019, 1:14 AM
