and 
Prove that
Let 
and 
Prove that
prove that![\[ \frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{d^2} + \frac{d^2}{a^2}\geq\frac{a}{d} + \frac{b}{a} + \frac{c}{b} + \frac{d}{c}\]](http://latex.artofproblemsolving.com/0/0/4/004e7f148bbb0c797688f5195aa4002dbc316470.png)
If you know same tasks, link them please
Prove that
Let 
Prove that
Let 
and 
Prove that
Let 
Prove that
be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
(
well). i want to study so if you guys have some easy or normal problems please send me
,
,
,
,
.
.
be reals such that 
Prove that
Where 
and 
Prove that 
.
Prove that 
,
,
Point 
is chosen on the circle with radius 
is chosen on the circle with radius 
is chosen on the circle with radius 
,
in terms of 
.
of moving 
unit in the positive direction and probability 
of moving 
.
Y by
Initially, two constant polynomials are written on the board: 
and 
. At each step, it is allowed to add to one of the polynomials and to multiply another one by the polynomial 
. Can the polynomials become equal at some point?
Proposed by Oleksii Masalitin
and 
. At each step, it is allowed to add to one of the polynomials and to multiply another one by the polynomial 
. Can the polynomials become equal at some point?Proposed by Oleksii Masalitin
This post has been edited 1 time. Last edited by mshtand1, Yesterday at 12:47 AM
?
which is even.
and 
.
and 
.
,
means that 
was multiplied by 
.
