cause there are 10 ways to choose 1 element that will be repeated. Similarly for 2 same elements it would be 
the answer would be ![$(2^{10}-1)-([A_1+A_3+A_5+A_7+A_9]-[A_2+A_4+A_6+A_8+A_{10}].$](http://latex.artofproblemsolving.com/7/3/1/73130cab8af6ffb5c2638548fdf6af3ecc70a6ed.png)
But this number turned out to be 
But I realized that 
So I was really confused of why i got the right answer somehow in my calculations.
and 
then find the greatest possible value of 
be positive real numbers that fulfill![\[
\frac{x^2}{y^2}+\frac{4x^2-3xy-4y^2}{2xy-5y^2}=2
\]](http://latex.artofproblemsolving.com/6/c/c/6ccba85deb3e6aa205abd3bc8e9e9bb68f4df6fd.png)
Hence find the value of 
Y by
Let P be a point in a square ABCD. The lengths of segments PA, PB, PC are 17, 11 and 5 respectively. Determine the area of the square and if it can’t be determined exactly, all possible values are to be listed.
German math Olympiad, Class 9, 2024
It’s my first time posting - please excuse any mistakes
German math Olympiad, Class 9, 2024
It’s my first time posting - please excuse any mistakes
be the foot of the altitudes from 
to 
.
,
.
from 
and subtracting 
,
and 
in terms of 
,
.
