[/quote]
,
such that 
.
be positive real numbers such that 
and 
,
help in one of my classrooms, and one of the Halpers posted. Is this a glitch or a bug(see screenshot)?
be a graph colored using 
colors. We say that a vertex is forced if it has neighbors in all the other 
colors.
-
colors such that at least 
of the colors have a forced vertex of that color.
vertices of the same color may be adjacent.
be positive real numbers. Prove the inequality![\[
\frac{x_1 + 3x_2}{x_2 + x_3}
\;+\;
\frac{x_2 + 3x_3}{x_3 + x_4}
\;+\;
\frac{x_3 + 3x_4}{x_4 + x_1}
\;+\;
\frac{x_4 + 3x_1}{x_1 + x_2}
\;\ge\;8.
\]](http://latex.artofproblemsolving.com/5/c/0/5c062a37f6ff120232ae87eb0093a4ce73ee0eb1.png)
,
is a positive integer.
with exactly 
elements such that the sum of its elements is a prime number.
with at most four natural divisors, which have the property that for any two distinct proper divisors 
and 
of 
,
divides 
satisfying the equation 
with complex coefficients such that 
for any complex number 
Y by Mango247, Mango247
For my writing problem in my Calculus class, the text box for the response can be adjusted with a little thingy in the bottom right corner. Using the thingy, you can extend the text box past the side of the page and make it so some of your response cannot be seen. It goes away when you save the problem and click edit again, but I thought it was worth mentioning.
Thanks.
edit: testing other bug
Thanks.
edit: testing other bug
This post has been edited 2 times. Last edited by TheHawk, Nov 13, 2022, 10:22 PM
