. Prove that
have real roots and real coefficients with 
.
?
,
.
have roots 
.
.
(I won't be proving this here). This new information allows us to utilize the mean inequality chain as follows:
Similarly, applying AM-HM yields 
.
.
and 
Show that
Let 
Show that
such that 
is a perfect cube.
digits are distinct?
Solve for 
,
,
,
.
be the point on 
such that 
,
be the midpoint of 
.
is a point such that 
is a rectangle, compute the area of 
.
has a sidelength of 
,
,
are chosen on 
,
,
,
,
,
are length 
.
.
satisfies for all integers 
,
If 
and 
,
.
children have black hair, all but 
have red hair, and all but 
have blond hair. How many children are there in the class?
can be partitioned into n Akash subsets.
be a prime number. How many different pairs 
satisfy the equation:
:
.
Let 
.
,![$ x \in [-1 / 10,0] $](http://latex.artofproblemsolving.com/1/e/f/1ef43e8c80ca68c6262a0f96555efb0a00e531d1.png)
.
is the inverse function of 
]
Y by Yrock, Exponent11, PikaPika999
Summary of the problem: When using exit() (or quit()) in the Python windows on AoPS the "Description" and "To fix" options show up as "undefined"
Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A
Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A
Attachments:
This post has been edited 2 times. Last edited by SoaringHigh, Oct 22, 2024, 2:11 PM
