if
,
,
?
,
,
in terms of 
.
.
to z because we already know the value of 
.
(in the equation 
)
.
.
and cross multiply.
.
.
![\[
x^2 + 2|x| - 6x + 15 = 0.
\]](http://latex.artofproblemsolving.com/1/1/d/11dbf7a605e8c49bb730eb0bd3737019b277fa41.png)
(Note: the modulus of a complex number 
is 
.
and 
.
and 
.
.
![\[
\frac{ab + bc + ca}{a^2 + b^2 + c^2} + \frac{1}{6} \left( \frac{(a - b)^2}{a^2 + b^2} + \frac{(b - c)^2}{b^2 + c^2} + \frac{(c - a)^2}{c^2 + a^2} \right) \leq 1.
\]](http://latex.artofproblemsolving.com/d/8/b/d8b3869addff6715d86b73083c77395d64ab1995.png)
are the 256 roots (not necessarily distinct) of the equation 
,
.
such that 
,
,
,
are real numbers that satisfy the system of equations
and 
.
?
,
for the same reason.
and 
.
.
.
,
,
as it is also equal to 
and 
.
but once again substitute 
with 
with 
.
,
.
and 
Prove that
Y by
Howdy!
I'm in Calculus 3556. I remember seeing something that said if I email someone, I can ask for longer access to the course page? I would like to have the materials from class up until I take the AP Exam in mid May. I'm assuming I would need to email Student Services? Would that be studentservices@aops.com?
Thanks!
I'm in Calculus 3556. I remember seeing something that said if I email someone, I can ask for longer access to the course page? I would like to have the materials from class up until I take the AP Exam in mid May. I'm assuming I would need to email Student Services? Would that be studentservices@aops.com?
Thanks!
